The functional reconstitution technique is used for the first time to theoretically and a priori assess the numerical performance of Reissner’s Mixed Variational Theorem in the case of linear quadrilateral finite element, Generalized Unified Formulation, and composite materials. From the finite element discretization, the semi-complementary energy is reconstructed in integral form. Analytical expressions for the exact and spurious terms are obtained. Using the elasticity solution for a simply supported plate, it is numerically shown that these spurious contributions do not significantly alter the quality of the approximation of the total level of energy, with overall excellent computational performance. On the other hand, when the starting functional is the strain energy and the principle of virtual displacement is adopted, the finite-element-introduced additional terms and in particular the contributions associated to the transverse shear stresses are demonstrated to add a very large error, which is a priori proven to be eliminated with selective integration. The presented technique could be extended to analyze the performance of other finite elements (e.g., higher-order triangular ones) within Reissner’s Mixed Variational Theorem and Generalized Unified Formulation.
Functional Reconstitution of Reissner’s Mixed Variational Theorem for Finite Element Applications
AIAA Journal ; 57 , 8 ; 3534-3547
2019-05-29
14 pages
Aufsatz (Zeitschrift)
Elektronische Ressource
Englisch