# Chap 2 Introduction to the Stiffness - DOC

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```					CE 631      Chapter 2 Introduction to the Stiffness Method                          page   1

Chap 2 Introduction to the Stiffness
(Displacement) Method
Given:
Structure dimension
Material
Support (boundary) conditions
Reaction forces
Internal forces
Displacements
Basic Unknowns:
Nodal Displacements (in global coordinates)

Primary Structures:
Single members (elements) in a structure

Slop-Deflection Equation for a Member (Element):
It relates the unknown nodal displacements to the nodal internal forces, in a
matrix form: k d = f
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CE 631        Chapter 2 Introduction to the Stiffness Method                          page   2

Element Stiffness matrix:
For an element (member), a stiffness matrix is a matrix such that
kd=f
where k relates local-coordinate nodal displacements d to local forces f of single
element.

Global Nodal Equilibrium Equations for a Structure:
KD=F
where K relates global-coordinate nodal displacements D to global forces F at
nodes of a structure. K is assembled from Element Stiffness Matrix k.

General Procedure:
   Select Element Type
   Assume Displacement Functions
   Define Material Properties
   Derive the Element Stiffness Matrix
   Assemble the Element Equations to the Global Equations
   Boundary (support) Conditions
   Solve for Node Displacements
   Solve for Internal Forces

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CE 631      Chapter 2 Introduction to the Stiffness Method                           page   3

Basic Assumptions (for the following Chapters in the Text book):
A. Small deformation and strain:

The deformations of the structure must be so small that the geometry of the
structure must not undergo significant change. The dimension can be based on
the undeformed geometry of the structure. The strain calculation can be based
on the First Order Theory.

B. Linear-elastic Material:

The structure must be composed of linearly elastic material so that the simple
linear material model can be used.

 Throughout this text, these two basic assumptions will be used.
 Purpose: to make the concepts of (Linear) Finite Element Analysis easy to
understand in the First Course of Finite Element Methods.

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