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The Essentials of Finite Element Modeling and Adaptive Refinement by John O. Dow

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APPENDIX 2B

EXACT SOLUTIONS FOR TWO LONGITUDINAL BAR PROBLEMS

2B.1 INTRODUCTION

This Appendix presents the exact solution for a bar fixed at both ends and deformed by two relatively simple distributed loads: (1) a constant load and (2) a linearly varying load. These loads are shown in Fig. 2.3 in the main body of this chapter. They are reproduced here for the convenience of the reader as Fig. 2B.1.

The form of the governing differential equation presented here differs slightly from the form shown in some presentations. In this case, the positive load is on the left-hand side of Eq. 2B.1. This sign on the applied loading occurs when the governing equation is derived using equilibrium or the Calculus of Variations. In some presentations, the ...

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