Governing Equations and Solutions for Linear Elasticity

The essential governing equations for a Unear elastic body are given below. In these equations the position variable, x, is exphdtly shown to emphasize that in multidimensional problems the stress and strain fields vary spatially in the material. 

The governing equations 9.25, 9.26, 9.27 comprise 15 coupled partial differential equations in 15 unknowns which are to be solved based upon the boundary conditions (Eq. 9.28). As can be seen from Eqs. 9.28, there are several types of boundary value problems that can be formed  

Traction BVPs Loading is applied through prescribed surface tractions. 

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