Abstract
A numerical solution technique named as variational differential quadrature (VDQ) is adopted herein for the compressible nonlinear elasticity problems. The governing equations are obtained based on the virtual work principle by considering displacement as the unknown field. The neo-Hookean model is also considered for the hyperelastic behavior of material. In the solution method, an efficient vector–matrix formulation is developed from which the discretized governing equations are achieved from the weak form of equations in a direct approach. Simplicity in implementation and accuracy are among the features of the proposed approach. Moreover, it does not suffer from the locking problem and unphysical instabilities. Fast convergence rate and computational efficiency are other advantages of this method. A number of numerical examples are given to reveal the good performance of VDQ in the large deformation analysis of compressible and nearly-incompressible bodies.
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