Construction of stiffness matrices of volumetric finite elements by the double approximation method and software verification

Numerical solution to problems of the theory of elasticity in the three-dimensional formulation with the finite element method envisages the finite elements introduction in the form of parallelepipeds, prisms and tetrahedra. As a rule, construction of the volumetric finite elements stiffness matrices is based on the isoparametricity principle. In calculation practice, the so-called multilinear isoparametric finite elements with linear law of the geometric characteristics and displacement approximation are most widely used. The main disadvantage of such elements lies in the locking effect when simulating the flexural deformations. Moreover, the numerical solution error increases significantly, if the structure compared to conventional deformations undergoes significant displacement as a rigid whole. The volumetric multilinear finite elements were constructed (based on the double approximation method) and tested making it possible to simulate the structure behavior under various types of the external influences.

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