AERO 306 Study Guide - Final Guide: Kolmogorov Space, Airbus, The Technique

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The goal now is to develop a systematic procedure for obtaining approximate solutions. Uniaxial bars and beams will be used to illustrate the basic concepts. To refresh your memory, we will begin by solving a uniaxial bar problem using just differential equations. The equilibrium equation can be derived by imposing equilibrium on a differential slice of the bar as follows. This equation is valid for any uniaxial rod even if the cross sectional area or material properties are functions of x. constitutive relations enter the picture when we express f in terms of displacement. For example, if the material is thermoelastic, then we would substitute. F = internal force, not applied force (remember cauchy"s formula) Assume: ea constant f=constant no thermal effects f du dx. Now impose the boundary conditions (0) 0 u and. Assume some variation of temperature along the length and re-solve this problem. There are various ways to derive the virtual work equation for a uniaxial bar.

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