F inite Element Method. for readers of all backgrounds. G. R. Liu and S. S. Quek. CHAPTER 4:. FEM FOR TRUSSES. CONTENTS. INTRODUCTION FEM EQUATIONS Shape functions construction Strain matrix Element matrices in local coordinate system Element matrices in global coordinate system
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for readers of all backgrounds
G. R. Liu and S. S. Quek
FEM FOR TRUSSES
Note: Number of terms of basis function, xn determined by n = nd- 1
At x = 0, u(x=0) = u1
At x = le, u(x=le) = u2
Note: ke is symmetrical
Note: me is symmetrical too
(Relationship between local DOFs and global DOFs)
Transformation applies to force vector as well:
Recovering stress and strain
Consider a bar of uniform cross-sectional area shown in the figure. The bar is fixed at one end and is subjected to a horizontal load of P at the free end. The dimensions of the bar are shown in the figure and the beam is made of an isotropic material with Young’s modulus E.
Exact solution of
(1 truss element)