Static and Dynamic Stresses

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A Guide to

Linear Static and Dynamic Stress Analyses

Click Here to Get Star ted with Algor’s Click Algor’s InCAD DesignPak at www.feaincad.com DesignPak www.feaincad.com Algor’s InCADPlus family of products provides a new level of seamless CAD/CAE interoperability with popular CAD solid modelers such as SolidWorks, Mechanical Desktop, Pro/ENGINEER and Solid Edge. InCADPlus captures the exact assembly or part geometry utilizing the CAD solid modeler’s application programming interface, thus eliminating data translation problems. When Algor and the CAD solid modeler reside on separate computers, Algor's Direct Memory Image Transfer (DMIT) technology can achieve the same level of interoperability. Algor’s CAD/CAE interoperability products connect to every modeling, FEA and MES product offered by Algor. Algor also supports CAD standard neutral (universal) files, including IGES, ACIS, Parasolid and STL.

CAD/CAE Interoperability

Finite Element Modeling
Superdraw III, Algor's precision finite element model-building tool, offers many design scenarios and mesh enhancement capabilities. Algor enables several design classes, including 2- and 3-D surface and solid models, beam or truss and plate/shell. Algor also enables engineers to build compound models having mixed element types. Superdraw III provides access to Merlin Meshing Technology for automatic surface mesh enhancement or enables engineers to work directly on an FEA model surface for manual mesh enhancement. Engineers can choose tetrahedral, brick or hybrid (bricks outside and tetrahedra inside) solid FEA meshes.

Other Algor Capabilities

Multiphysics
Algor offers heat transfer, fluid flow and electrostatic analysis capabilities that can be performed separately or in combination to analyze the effect multiple physical phenomena have on an object’s behavior. Multiphysics is important since real-world mechanical behavior is often the result of not one, but several, physical factors acting simultaneously. Algor's multiple processors can share the same geometry file which links to a centralized material database eliminating the need to duplicate modeling efforts for different analyses. In addition, visualization capabilities enable the engineer to see the combined effects of multiple physical phenomena and evaluate the accuracy of analyses.

Mechanical Event Simulation and Kinematic Elements
Use Mechanical Event Simulation (MES) and Algor’s proprietary kinematic element technology to simultaneously replicate motion and flexing for linear and nonlinear events involving complex mechanical assemblies. Using kinematic elements to reduce computation time, engineers can determine stresses at all times during an event and see if a device will twist, stretch, squash or buckle through real-time What-You-See-Is-What-You-Get visualization that even non-engineers can understand. The use of physical data, not assumptions, leads to accurate results and reduces the need for physical prototype testing. MES does not require internal dynamic loading input; thus, it eliminates the need to determine forces by external calculation or testing. Click Here to Learn More about PipePak Click PipePak Piping Design and Analysis Design and Analysis at www.pipepak.com Analysis www.pipepak.com PipePak enables the design of piping systems using Superdraw III, the traditional spreadsheet interface or both. PipePak includes a comprehensive selection of analysis capabilities, supports wellknown piping codes and has advanced visualization tools. In addition, PipePak's Report Wizard can create reports in an Internet browser-based format for quick viewing, printing and distribution.

lgor’s linear static and dynamic stress analysis On the Cover capabilities determine stresses, displacements and natural frequencies as well as predict dynamic response to static and dynamic loading. These capabilities are highlighted throughout this brochure. Algor’s FEA, Mechanical Event Simulation, modeling and CAD/CAE interoperability tools are designed to help engineers develop products that are more reliable and Linear static stress analysis less costly to produce with faster times-to-market. with composite materials was To provide the best cost/benefit solution for each cus- used to optimize this bike frame. See page 9. tomer, Algor’s High Technology Core Packages and Extenders can be purchased at special combination pricing or separately to best fit individual needs while allowing for future growth and change. See page 13 for more information about Algor’s product line.

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In This Brochure
Linear Static Stress Analysis
Linear Static Stress Analysis...................................................................................2

Dynamic Stress Analyses
Linear Natural Frequency (Modal) Analysis...........................................................3 Linear Transient Stress Analysis by Modal Superposition....................................4 Linear Transient Stress Analysis by Direct Integration.........................................4 Response Spectrum Stress Analysis.....................................................................5 Dynamic Design-Analysis Method..........................................................................5 Eigenvalue Buckling Analysis for Beam and Plate/Shell Models.........................6 Linear Natural Frequency (Modal) Analysis with Load Stiffening for Beam and Plate/Shell Models..........................................6 Random Vibration Stress Analysis using Power Spectral Density.......................7 Frequency Response Stress Analysis....................................................................7

In This Brochure

Auxiliary Features
Weight, Center of Gravity and Mass Moment of Inertia.........................................8 Internal Forces Calculator.......................................................................................8 Gap/Cable Elements for Linear Static Stress Analysis..........................................9 Composite Materials................................................................................................9

CAD/CAE Interoperability and Finite Element Modeling
CAD/CAE Interoperability......................................................................................10 Finite Element Modeling........................................................................................10

Analysis Visualization
Built-In Analysis Visualization...............................................................................11 Monitor Utility.........................................................................................................11

Finite Elements for Linear Static and Dynamic Stress Analyses
Finite Elements for Linear Static and Dynamic Stress Analyses......................12

Algor Product Line
High Technology Core Packages...........................................................................13 High Technology Extenders..................................................................................13

Web Courses and Webcasts
Web Courses and Webcasts....................................................................Back Cover

inear static stress analysis is the most common type of FEA used today. Industrial products, manufacturing, consumer products, civil engineering, medical research, power transmission and electronic design are just a few of the areas in which linear static stress analysis is often performed.

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Linear Static Stress Analysis
Linear static stress analysis, included in all of Algor’s High Technology Core Packages, enables the study of stress, strain, displacement and shear and axial forces that result from static loading. This analysis type is often sufficient for situations in which loads are known and the Team SABCO, Mooresville, time of peak stress is evident. NC, employed linear static When performing a linear stastress analysis to improve tic stress analysis, engineers the handling of its NASCAR apply static loads, such as forces race cars. Based on the pressures, or known Algor deflection results, the team modified the rear or chassis design, achieving a 25 percent gain in stiff- “imposed” displacements to a ness. This will make the car easier to handle in finite element model. Then they turns, enabling the driver to maintain higher speeds. add elastic material data, boundModel and photo courtesy of Team SABCO. ary conditions and other information such as the direction of gravity. Static forces are assumed to be constant for an infinite period of time while resulting strain, movement and deformation are small. Engineers assume that the material will not deform beyond its elastic limit and any resulting dynamic effects from the loading are insignificant.
NASCAR Winston Cup Racing Team Optimizes Car Handling and Stability Engineer Solves Mysterious Failure of Mountain Bike Component Design
Professional mountain bike riders must develop a strategy for how best to maneuver through courses of steep hills, boulders and ravines and do it faster than their competitors. While the best cyclists are skilled, experienced and physically fit, they also depend on reliable, lightweight equipment. Rond Products B.V. of Ingen, Holland, created a new front fork design made of a lightweight magnesium alloy; however, cracking occurred under normal loading conditions. Engineers at Bosch Engineering, Oldenzaal, The Netherlands, modeled the front fork with Solid Edge and used Algor’s linear static stress analysis software to determine the cause of the failure. The analysis showed that the cracking was due to the part design, not the material properties of magnesium as was expected. The critical loading was primarily a function of braking and horizontal/vertical loading of the front wheel. The engineers modified the shape of the design and wall thickness while maintaining the look and weight of the component. Rond Products’ design cycle and time-to-market were drastically reduced with the help of Algor FEA. • phone: +1 (412) 967-2700 • fax: +1 (412) 967-2781 •

Linear Static Stress Analysis

Model and photos courtesy of Bosch Engineering.

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he Vibration Extender options add linear natural frequency (modal) analysis, linear transient stress analysis by modal superposition for low frequencies, linear transient stress analysis by direct integration for high frequencies and response spectrum stress analysis and Dynamic Design-Analysis Method (DDAM) for response to sudden forces. Eigenvalue buckling analysis for beam and plate/shell models, linear natural frequency (modal) analysis with load stiffening, random vibration stress analysis using power spectral density and frequency response stress analysis to predict response due to single frequency waveforms are also included.
Algor’s physics-based Accupak/VE Mechanical Event Simulation software simultaneously simulates dynamic motion and flexing of mechanical devices and computes stresses over time during an event. Accupak/VE adds value to dynamic stress analyses by offering both linear and nonlinear material models, handling body-to-body contact with contact elements and impact surfaces and computing changing stiffness values over the course of an event. Accupak/VE is physics-based so that engineers do not need to be experts in vibration theory or make assumptions about internal dynamic loads to get accurate analysis results. Contact your Algor account representative for more information.

Dynamic Stress Analyses

Linear Natural Frequency (Modal) Analysis
Linear natural frequency (modal) analysis is used to determine a part’s natural frequency and natural vibration mode shapes. This application is critical in virtually every type of engineering design because of the disastrous consequences of resonance within design parts. For example, if a power-driven device such as a motor produces a frequency at which an attached structure naturally vibrates, resulting resonance may destroy the attached structure. The results of linear natural frequency analysis are often used as input for other dynamic stress analyses.
FEA Gets Porsche Motor Production Up and Running Faster
An engineer at Speedy Engineering of Germany used Algor’s linear natural frequency analysis software to test for resonant frequencies in several components of a production line at Dr. h.c. Ferdinand Porsche AG in Germany. Porsche contracted KTW Konstruktion Technik K. Weißhaupt GmbH to produce the cast iron fixtures, which hold automobile motor parts in place during drilling and high precision milling. If the new fixture components or motor parts have resonant frequencies resembling those of the machining tool, the part surface may become too rough and unusable. Therefore, the engineer had to choose machining frequencies that would not cause resonance. For the linear natural frequency analysis, the engiTop Left: The completed fixture. neer fully constrained the fixture at the six mounting Bottom Left: The first three points on the palette and computed the first 30 eigenvibration modes correlated frequencies. Based on the analysis results and closely with test data. accounting for variations in the stiffness of cast iron, the engineer recommended a practical frequency Model and photo courtesy of Speedy Engineering. window width between 25Hz to 40Hz. • e-mail: info@algor.com • www.algor.com •

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Linear Transient Stress Analysis by Modal Superposition
Linear transient stress analysis by modal superposition (time history) uses mode shapes and natural frequencies calculated through a linear natural frequency analysis to solve for time-varying loads at low frequencies. Engineers can produce the dynamic response of a structure subjected to forces, moments, temperatures or boundary accelerations. Furthermore, ground acceleration components can be added in any or all three of the global direcAntenna Analyzed with Algor tions to determine dynamic responses An Italian engineering consulting such as deflection, velocity, accelerafirm in Bologna, Italy, used linear transient stress analysis by tion and stress versus time. modal superposition to redesign Modal superposition excludes the an 85-foot antenna so that it effects of high frequency modes; thus, would support a group of rotating it uses only low frequency modes of antennas at its top. The analysis vibration and requires fewer calculasimulated an impulsive wind load acting in resonance with the lowtions. This type of analysis is used for est natural frequency for the new fluid flow, structural vibration and antenna group on top. The group load testing. For example, the effects of antennas was added to deterof impulsive wind loading on towers mine the source of interfering or sinusoidal loading on air purificaradio transmissions. Model courtesy of Studio Tecnico Zocca. tion equipment can be determined.

Dynamic Stress Analyses

Linear Transient Stress Analysis by Direct Integration
Similar to linear transient stress analysis by modal superposition, linear transient stress analysis by direct integration is used to analyze the results of dynamic impact such as when a stone hits a windshield. However, in this case, direct integration is used for higher frequencies with higher damping values instead of modal superposition for low frequencies. Thus, engineers do not need to perform a linear natural frequency analysis.
Pittsburgh’s Smithfield Street Bridge Renovated using Algor
The Smithfield Street Bridge renovation undertaken by Mackin Engineering of Pittsburgh, PA, included removing the trolley tracks and providing for three lanes of traffic, with the center lane changing directions depending on traffic volume. Mackin engineers had to examine vibration and natural frequency. Engineers first determined the bridge's natural frequency by performing an analysis on several structural models, including the existing structure and three alternatives. Then, an analysis using direct integration with time-varying loads was performed to determine maximum stresses for selected truss members and maximum truss deflection. Mackin engineers were able to efficiently determine possible replacement options based on analysis results. In selecting a replacement for the aluminum flooring system and deck, dating back to 1933, engineers found that the bridge would be affected little by the type of flooring system chosen. Therefore, they selected the least expensive system feasible—a filled steel grid deck—which also required the lowest future maintenance. • phone: +1 (412) 967-2700 • fax: +1 (412) 967-2781 •

Top: The Smithfield Street Bridge undergoing renovation. Bottom: This analysis shows stresses determined using direct integration and time-varying loads.
Model and photo courtesy of Mackin Engineering.

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Response Spectrum Stress Analysis
Engineers use response spectrum stress Wheeling Suspension Bridge analysis to determine structural Analyzed with Algor response to sudden forces or shocks that occur at fixed boundary points. Responses include maximum stress, acceleration, velocity, displacement, force, moment and torque. During an earthquake, violent shaking is transmitted into a structure at points where it is attached to the ground. To help engineers design sound Researchers from West Virginia University, structures, response spectrum stress Morgantown, WV, conducted a series of analysis is used in conjunction with response spectrum stress analyses on the information gathered by instruments Wheeling Suspension Bridge in Wheeling, from past earthquakes. An engineer can WV, to determine how it would respond to determine how a structure would react seismic activity. Using data based on historic earthquakes in the region, the analyses to a past real-world earthquake and con- showed localized damage to floor beams and sider this in any new design. diagonal floor ties at the east tower and the Response spectrum stress analysis top chords of the stiffening truss at mid-span. can also help engineers design compo- The localized failure in the bridge deck could nents for nuclear power plants, such as be avoided through reinforcements. Model courtesy of West Virginia University. nuclear reactor parts, pumps, valves, piping and condensers. Algor’s response spectrum stress analysis uses formulae recommended by the U.S. Nuclear Regulatory Commission.

Dynamic Stress Analyses

Dynamic Design-Analysis Method

Algor’s Dynamic Design-Analysis Method (DDAM) processor enables engineers to analyze a model using this U.S. Navy procedure for shock design. All mission-essential equipment onboard surface ships and submarines must be qualified for shock loads, such as from depth charges, mines, missiles and torpedoes. Engineers can use DDAM to analyze the shock response at the mountings of shipboard equipment such as masts, propulsion shafts, rudders, exhaust uptakes and other critical structures. DDAM is a shock hardening program that estimates the dynamic response of a component to a shock loading caused by the sudden movement of the ship. Derived from response spectrum stress analysis, which is used primarily to study responses to earthquake loading, DDAM simulates the interaction between the shock-loaded component and its fixed structure. The free motion of a ship in water will produce a higher shock spectrum than would a heavy structure Algor’s DDAM can determine the effects of shock wave on ground. DDAM takes into account this effect in input on ship components, relation to the weight of the equipment and mounting such as the hull of this ship. location and orientation of the equipment on the ship. Photo courtesy of the Results include maximum stress, acceleration, velocIngalls Shipbuilding division ity, displacement, force, moment and torque. of Litton Industries. • e-mail: info@algor.com • www.algor.com • Page 5

Eigenvalue Buckling Analysis for Beam and Plate/Shell Models
In the normal use of most products, buckling can be catastrophic if it occurs. The failure is not one of stress but of geometric stability. Once the geometry starts to deform, it can no longer withstand even a fraction of the force initially applied. Buckling analysis is used to determine if a specified set of loads will cause buckling and the shape of the buckling This thin-walled soda mode. This type of analysis is useful in situations where a can shows geometric failure of a plate/shell beam is subjected to an axial load or when a thin-walled plate model under pressure. or shell model undergoes edge compression. Engineers can then design supports or stiffeners to prevent local buckling. Forces causing local buckling include changes in temperature and temperature distribution, acceleration and pressure due to force. Note: Accupak/VE Mechanical Event Simulation can be used for Left: The original shape of the high tower. Center: The displaced shape shows localized local buckling situations where perbuckling. Right: The displacement results manent deformation due to material show highest displacement in red. nonlinearities is expected.

Dynamic Stress Analyses

Linear Natural Frequency (Modal) Analysis with Load Stiffening for Beam and Plate/Shell Models

Load stiffening produces changes in the natural frequency of an object that result when a force is applied to it. This analysis type uses a stressdependent stiffness matrix to compute natural frequencies and mode shapes. Linear natural frequency analysis with load stiffening can be applied to any part subjected to dynamic loading. Because natural frequencies change as applied forces While the mode change, engineers must use load shapes for each analystiffening to receive accurate analysis are the same, a sis results. It can also determine vast difference exists how force and frequency relate. between the frequencies for each analysis. One example is a guitar string. Plucking a guitar string causes the string to produce a certain frequency or tone. Tightening or loosening the guitar string changes its natural frequency. If the cross-sectional area, applied force, length and mass density are specified, this processor will determine the frequency of the string due to load stiffening. Page 6 • phone: +1 (412) 967-2700 • fax: +1 (412) 967-2781 •

Random Vibration Stress Analysis using Power Spectral Density
The vibration generated in vehicles from motors, road conditions or from rocket and jet engines, to name a few sources, is a combination of many frequencies and has a certain "random" nature. Random vibration stress analysis determines how the structure of an object or a supported object reacts to constant, random vibration. Random vibration stress analysis uses input from linear natural frequency analysis and power spectral density curves, which are representations of vibration frequencies and energy in a statistical form. The analysis determines the root-meansquare response of displacement and stress resulting from constant, random vibration over time. This information can help discern the structural integrity of a vehicle and the effects of vibration on payloads being transported by a vehicle.
NASA Satellite Reaction Wheel Optimized with Algor
NASA scientists rely on reaction wheels to maneuver observation satellites in space. Based on information gathered by sensors, four reaction wheels position the satellite to face constellations of interest. The reaction wheels must withstand rocket launch Top: The housvibrations to operate ing deflects effectively in orbit. due to random Engineers at the vibration during launch. Left: The NASA Goddard Space reaction wheel's motor. Flight Center, Rendering, model and photo courtesy of The redesigned reaction Greenbelt, MD, used NASA Goddard Space Flight Center. wheels were launched random vibration stress successfully on the analysis to test the structural integrity of a redesigned reaction Transition Region and wheel that can position satellites more quickly. NASA simulated Coronal Explorer vibration forces during a rocket launch and analyzed deflection (TRACE), a satellite mission that is studying in the reaction wheel's outer housing structure. NASA then optimized the housing's design to reduce deflection that would the sun's coronal otherwise cause the reaction wheel to fail. region.

Dynamic Stress Analyses

Frequency Response Stress Analysis
Frequency response stress analysis analyzes the steady-state operation of a machine, vehicle or process equipment design subjected to continuous harmonic loading. As compared to the general linear transient stress analysis modules, frequency response stress analysis provides an easy, quick method in which the only inputs are a constant frequency and amplitude. The analysis determines stress, displacement and the phase angle at each mode along with a square-root-sum-of-the-squares response based The structural response of buildon steady-state inputs. ing components such as walls, For example, this analysis type could be used to floors and support beams to the vibrations of large generator determine the vibration effects of a washing motors or processing systems is a machine with an unbalanced load or a bent wheel common application of frequency response stress analysis. on a vehicle. • e-mail: info@algor.com • www.algor.com • Page 7

n addition to linear static and dynamic stress analysis capabilities, Algor has several auxiliary features that add to the individual processors. These features include: the weight, center of gravity and mass moment of inertia processor, the internal forces calculator, gap/cable elements and composite materials analysis.

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Weight, Center of Gravity and Mass Moment of Inertia
The weight, center of gravity and mass moment of inertia processor calculates the center of gravity, mass moment of inertia, weight and volume of an FEA model. Because the processor can determine the weight and volume of a final design for any analysis type, engineers can easily use an iterative process to determine the cost or amount of material needed. The volume and weight can be calculated in just seconds after each design modification. Furthermore, knowing the center of gravity and mass moment of inertia is invaluable when performing rigid-body dynamics. The properties of this mouthpiece (right) were calculated in about 30 seconds using the processor. Because of the part’s irregular curves, finding its volume alone through hand calculations may have taken several hours.

Auxiliary Features

Algor’s weight, center of gravity and mass moment of inertia processor was used to determine properties of this dive suit mouthpiece.

Internal Forces Calculator
The internal forces calculator is typically used to obtain reaction forces for all nodes at constrained locations without using boundary elements. It provides a faster means of determining reaction forces by summing up forces at all nodes. At nodes with no resisting constraint, no reaction forces are present; thus, the sum of reaction forces at these nodes will be zero. A more powerful use of the internal forces calculator is in submodeling or substructuring, when an engineer builds a large model by modeling its parts separately. By masking an element group from the model, engineers can determine the remaining forces that act upon the masked element group. Then, these forces can be applied as loadings in a separate model of the masked element group in order to study it in more detail. The internal forces calculator can be used in the design of transport structures. For example, an airplane body was transported on a support structure by train. Aerospace engineers had to ensure that the body and structure would withstand a train wreck. At all reacting nodes, they examined how the load was distributed across the support structure. This information was used as loading in analyses of the airplane body.
• phone: +1 (412) 967-2700 • fax: +1 (412) 967-2781 •

This von Mises stress plot shows stresses resulting from an inward force on an impeller component.

This plot shows the summed reaction forces (highlighted with white circles) at the constrained locations that result from applied force.

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Gap/Cable Elements for Linear Static Stress Analysis
Gap/cable elements enable engiGap Elements used in Autoclave Design neers to analyze the interaction An Italian firm in Vicenza, Italy, used Algor FEA and between parts and the transfer of gap elements to design a high pressure autoclave. forces. This Algor Extender may The engineer needed to optimize the sealing properbe added to the linear static ties of the autoclave cover and shell prior to ordering materials and initiating manufacturing. stress processor. Sealing an autoclave vessel is accomplished by A gap element simulates com- inserting a flange, machined around the edge of the pression, where deflection door, into a ring at the top of the shell. The door is makes two nodes touch and then twisted so that a transmit force, such as when a series of teeth in the ball bearing moves in a joint. door frame are captured behind teeth in Using gap elements, engineers the shell ring. To can determine stresses, bending properly represent moments and axial forces where the nature of the compressive contact the bearing and joint meet. A cable element simulates between the two sets An engineer used 25 gap eleof teeth, 25 gap ele- ments to simulate the area of tension, where two nodes mov- ments were inserted contact between two suring away from each other a spec- at the area of faces of an autoclave. ified distance cause the element contact. Model courtesy of Belmonte ing. Claudio. to become active. Small deflections and strains exist, but with deflection-sensitive connectivity. Imagine a fishing boat in a river that is tied to a dock with a rope. A steady current causes the boat to pull away from the dock, creating stress where the rope is tied to the boat. This stress is transferred through the rope to where it connects to the dock. Cable elements let engineers measure stress at both ends of the rope. Other linear inputs, such as moment, temperature, acceleration and uniform and hydrostatic pressure, can be studied in conjunction with gap/cable elements.

Auxiliary Features

Composite Materials
Algor’s linear static and dynamic stress processors can use special elements to replicate the complex behavior of composite materials. These materials consist of two or more independent materials layered in different orientations to provide increased strength and lighter weight compared to what the individual materials acting alone can achieve. Algor offers two types of composite elements. Thin composite plate elements are based on the Kirchoff theory and support the Tsai-Wu maximum stress and strain failure criteria. These are used in structures such as bicycle frames and athletic equipment. Sandwich (thick) composite plate elements are based on the Mindlin plate theory and support the Tsai-Wu maximum stress and strain criteria. These are used in components for industries such as aerospace and automotive.
• e-mail: info@algor.com • www.algor.com •

Composite Bike Frame Analyzed with Algor

Composite Arts and Science, Ogden, UT, used composite materials to model this bike frame in order to achieve increased strength while maintaining a lighter weight. Composite frames are more comfortable and aerodynamic than traditional metal frames.
Model and photo courtesy of Composite Arts and Science.

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lgor’s CAD/CAE interoperability tools work seamlessly with popular CAD systems so that engineers can create high-quality FEA models from CAD designs using Algor’s suite of finite element modeling and analysis tools. A broad summary of these CAD/CAE interoperability and modeling capabilities are presented on this page. For additional information, refer to other Algor brochures.

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CAD/CAE Interoperability

CAD/CAE Interoperability and Finite Element Modeling

Algor’s CAD/CAE interoperability tools enable engineers to spend less time on CAD/CAE conversion and more time engineering quality products. The InCADPlus family of products works within popular CAD solid modelers such as SolidWorks, Mechanical Desktop, Pro/ENGINEER and Solid Edge to capture the exact assembly or part geometry in Algor with no file translation. Using Algor’s Working InCADPlus works within CAD Windows integration method, engineers simply select to capture the exact CAD the Algor meshing option from the CAD system geometry in Algor with no file translation. menu. The model appears automatically for surface meshing within Algor’s CAD Solid Model Interface. The InCADPlus family of products works same for all CAD solid modelers through easy-to-use icon toolbars that access all modeling, FEA and MES tools from the CAD system menu. Engineers save time by only learning one set of tools. When Algor and the CAD solid modeler reside on separate computers, Algor's Direct Memory Image Transfer (DMIT) technology can achieve the same level of interoperability. Algor also supports CAD standard neutral (universal) files, including IGES, ACIS, Parasolid and STL.

Finite Element Modeling
Algor offers fully-automatic modeling features and advanced modeling options for customization of FEA models to fit individual engineering needs. Superdraw III is both Algor's single user interface for FEA and a precision finite element model-building tool. It provides access to all of Algor's modeling and analysis tools. Superdraw III has the following Material properties for the interface features: gear are selected through the • A universal Model Data Control panel that Model Data Control panel. accesses data entry screens for defining element data and material properties, applying analysis parameters, verifying model integrity, running analyses, viewing results and more. • Live data checking against reasonable value limits. • Context-sensitive help for any data entry item. Superdraw III can be used with an automatic mesh engine to create 2- and 3-D surface and solid models, beam or truss designs and plate/shell models. Engineers can also build compound models having mixed element types. Accessed from Superdraw III, Merlin Meshing Technology offers mesh enhancement options for surfaces where high stresses most often occur. Algor’s solid mesh engines work from the surface mesh inward to create higher quality, less dense FEA solid meshes. Engineers can choose from three types of FEA solid meshing: brick, tetrahedral or hybrid (bricks on the model surface with tetrahedra inside).
• phone: +1 (412) 967-2700 • fax: +1 (412) 967-2781 •

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lgor’s built-in visualization capabilities provide a complete look at analysis results and enable engineers to graphically display results so that even nonengineers can clearly understand the implications of an analysis. Algor’s Monitor utility can be added for viewing time-dependent analyses. Visit www.algor.com to see Algor in action through free demonstration videos.

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Built-In Analysis Visualization

Click Here to Learn about Algor’s Click Algor’s NEW HTML Repor t Wizard Wizard

Algor’s built-in visualization capabilities enable engineers to view analysis results while providing information about analysis accuracy through a unified interface that supports all analysis types. Precision Engineers can create analysis replays and bitmaps Contour for presentations or reports to highlight areas of engineering concern. Results also can be extracted to provide step-by-step data for time-dependent analyses or automated iterative solutions. An exclusive precision contouring feature provon Mises vides qualitative and quantitative indications of the Stress Plot degree to which a model complies with finite element theory. For example, the precision contour (top) shows, in red, that a tighter mesh might increase accuracy around small holes at each end. A stress plot comparison (bottom) shows that von Mises stress concentrations in red coincide with the red areas of the precision contour. Similar to Monitor, Algor’s built-in visualization capabilities can be used to view time-dependent analysis results, including deflection, buckling and stresses, as they are processed. In addition, analysis replays can be created during processing for immediate viewing when processing is finished. Algor users can review the following engineering analysis results for linear static and dynamic stress analyses: • Twice the equivalent Tresca stress/strain • von Mises stress/strain • Maximum/minimum principal stress/strain • Stress/strain tensor • Magnitude of dot product vector • Nodal reactions vector • Beam/truss element-specific stress/strain • Gap and boundary element forces • Composite element-specific stress contour

Analysis Visualization

Monitor Utility
The Monitor utility, a virtual oscilloscope, can be added to dynamic stress analysis capabilities to make time-dependent results available graphically during processing. Engineers do not need to wait for an analysis to finish before reviewing results. Monitor plots results as curve data over time for easy interpretation, scrolling so the latest results are always displayed. Monitor shows displacement, velocity, acceleration, reaction forces and maximum stresses vs. time and can superimpose multiple curves into one Monitor plots window. An on-board Fast Fourier Transform ana- displacement lyzer converts displacement vs. time into frequen- vs. time for this beam as the analysis is processed. cy vs. energy for viewing frequency response. • e-mail: info@algor.com • www.algor.com • Page 11

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Finite Elements for Linear Static and Dynamic Stress Analyses

lgor’s finite element library includes many element types that can be combined for linear static and dynamic stress analysis models. The table below lists and describes available element types.
Description
Truss elements are used to provide stiffness between two nodes. These elements transmit compressive and tensile loads along their axis. Beam elements are used to provide elongational, flexural and rotational stiffness between two nodes. These elements can possess a wide variety of cross-sectional geometries including many AISC types.

Element Type Illustration
3-D Truss, 2-nodes

3-D Beam, 2-nodes 3-D Membrane Plane Stress, 3-nodes 3-D Membrane Plane Stress, 4-nodes 2-D Elasticity, 3-nodes 2-D Elasticity, 4-nodes 3-D Brick, 4-nodes

Membrane plane stress elements are used to model "fabric-like" structures, such as tents, cots, domed stadiums, etc. They support three translational degrees of freedom and in-plane (membrane) loading. Orthotropic material properties may be temperature dependent. Incompatible modes are available.

Elasticity elements are used for plane strain, plane stress and axisymmetric formulations. They support two translational degrees of freedom. Orthotropic material properties may be temperature dependent. Incompatible modes are available.

3-D Brick, 5-nodes

3-D Brick, 6-nodes

Brick elements are used to simulate the behavior of solids. They support three translational degrees of freedom as well as incompatible displacement modes. Applications include solid objects, such as wheels, turbine blades, flanges, etc.

3-D Brick, 8-nodes

3-D Plate, 3-nodes

3-D Plate, 4-nodes

Plate elements are used in the design of pressure vessels, electronic enclosures, automobile body parts, etc. They support three translational and two rotational degrees of freedom as well as orthotropic material properties. An optional rotational stiffness around the perpendicular axis is automatically added to the node of each element. Tetrahedral elements are used to model solid objects, such as gears, engine blocks and other unusually shaped objects. They support three translational degrees of freedom. They are also available in higher order formulations (mid-side nodes). Boundary elements are used in conjunction with other elements. A boundary element rigidly or elastically supports a model and enables the extraction of support reactions. Boundary elements are also used to impose a specified rotation or translation. Gap elements simulate compression, where deflection makes two nodes touch and transmit force, such as when a ball bearing moves in a joint. Cable elements simulate tension, where two nodes, moving away from each other to a specified distance, cause the element to become active.

Tetrahedral, 4-nodes

Boundary, 2-nodes

Gap/Cable, 2-nodes

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• phone: +1 (412) 967-2700 • fax: +1 (412) 967-2781 •

he Algor product line is arranged by High Technology Core Packages and Extenders. Core Packages contain varying levels of CAD/CAE interoperability, modeling, processing and visualization capabilities. Extenders provide added modeling and analysis capabilities to Core Packages. Please refer to the FEA and MES Software Pricing for Windows 95/98 and NT Workstations, call an Algor representative at +1 (412) 967-2700 or visit www.algor.com for more information.

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High Technology Core Packages

NEW Core and Extender Packages! Packag

Click View New When selecting a Core Package, engineers must choose Click Here to View our New Product Descriptions Product the modeling level and processing capabilities desired. Modeling Levels Algor’s wide range of modeling levels include the following capabilities: • InCADPlus for plugging into popular CAD solid modeler APIs to transfer exact CAD assembly and solid model geometry using Direct Memory Image Transfer. • Ability to import CAD solid models, assemblies and 2- and 3-D wireframes in CAD standard neutral (universal) file formats. • Surface and solid FEA modeling using Superdraw III. • Ability to include different element types in one model. • Enhanced, specialized beam element modeling. • Extended surface modeling with Supersurf. • Merlin Meshing Technology for surface mesh enhancement. • Automatic solid tetrahedral (four- or 10-node) FEA mesh generation. • Automatic solid brick (eight- or 20-node) or hybrid (combines bricks on the model surface with tetrahedra on the inside) FEA mesh generation. • Ability to export solid FEA models to third party FEA software. • Ability to import finite element models from other FEA packages. • Visualization with animation utility and complete post processing. Processing Capabilities • MECH/E: Linear static stress analysis and weight, center of gravity and mass moment of inertia processor. • MECH/MES: MECH/E, plus Mechanical Event Simulation for replicating motion and flexing with resulting stresses during linear events. • MECH/NLM: MECH/E, plus static stress analysis with nonlinear material models to predict deflection, deformation and displacement. • MECH/VE: The combined capabilities of MECH/MES and MECH/NLM. • MECH/MVE: MECH/VE, plus EAGLE, dynamic stress analysis, heat transfer and fluid flow analysis for multiphysics applications.

Algor Product Line

High Technology Extenders
Optional High Technology Extenders provide additional capabilities to the Core Packages. They also provide an outstanding value because they are specially priced and bundled for increased functionality. Some of Algor’s Extenders include: • Dynamic Stress Analysis • Accupak/MES • Accupak/NLM • Accupak/VE • Kinematic Elements • Heat Transfer Analysis • Fluid Flow Analysis • Electrostatic Analysis • Composite Materials • DDAM • Internal Forces Calculator • Gap/Cable Elements • EAGLE • ACIS Import Capability • PipePak Piping Design • Integrator for working • InCADPlus for working with CAD solid neutral files within CAD solid modelers • e-mail: info@algor.com • www.algor.com • Page 13

Web Courses Bring Algor Software Education to Your Desktop
Now new and experienced Algor users can get step-by-step instruction on how to take advantage of software features and capabilities without leaving their offices. Each 4hour Web Course registration includes: • Access to the live Web Course using a password. • Unlimited access to the replay of the Web Course for a personal screening at your convenience during a limited time period using streaming video format. • A video or CD-ROM containing the Web Course for your resource library. Algor's Web Courses have qualified for Professional Development Hours (PDH) within those states that have Continuing Professional Competency (CPC) requirements as a condition of license renewal for Professional Engineers. Visit www.algor.com/webcourse for scheduling and enrollment information.

Free, Public Webcasts Demonstrate Algor Software in Action
Join FEA software industry leaders every Tuesday at 10:00 a.m. Eastern Time in a live Webcast to learn more about Algor. These free, public Webcasts enable Algor to offer a higher level of service to our customers with state-of-the-art Internet audio/video technology. Each 1-hour Webcast covers: • General news about the main topic. • Frequently asked questions received by telephone or e-mail before and during the broadcast. • A main topic presentation showing Algor software in action. • A panel discussion on the main topic. Visit www.algor.com/webcast to view past live Webcasts or find out about future Webcast topics.

References
Learn more about Linear Static and Dynamic Stress Analysis capabilities through: Your Account Representative: +1 (412) 967-2700 Algor’s Linear Static and Dynamic Stress Analysis capabilities are continually expanding. This brochure may not represent the most recent capabilities. Ask your account representative about your specific requirements. Algor’s web site: www.algor.com Our web site offers the latest information on software products and services; live public Webcasts and replays showing Algor software in action; live Web Courses and replays for step-by-step instruction on using Algor software; analysis replays; limited-time trial software and tutorial downloads; accuracy verifications; the Algor Design World newsletter; upcoming education seminar schedule; and more! E-mail: info@algor.com DocuTech—Algor’s Software Documentation Information Resource on CD-ROM: Updated frequently and provided to all Algor customers, DocuTech contains software operating and reference documentation, educational materials, keystrokespecific tutorials, product information and more! Keystroke-Specific Tutorials: www.algor.com Available on our web site and DocuTech, these tutorials provide detailed, easy-tounderstand instruction on the most frequently used finite element modeling, engineering analysis and Mechanical Event Simulation capabilities. APD: +1 (800) 48-ALGOR The Algor Publishing Division offers books, videos and multimedia products which help engineers do better design, simulation and analysis with virtually any engineering software.

Algor, Inc.
150 Beta Drive, Pittsburgh, PA 15238-2932 Phone: +1 (412) 967-2700 Fax: +1 (412) 967-2781 California: +1 (714) 564-0844 Europe: +44 (1784) 442 246 E-mail: info@algor.com www.algor.com

When the Engineering Has to be Right
Algor software is subjected to U.S. nuclear power industry Quality Assurance standards.

Algor, Inc. is ISO 9001 compliant.
Part No. 3250.300 09/24/99 Copyright © 1999 Algor, Inc.


				
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