A Hybrid Displacement Boundary Element Formulation for Reissner Plate With Quadratic Elements

Abstract

Abstract. This paper presents the derivation of a new boundary element formulation for plate bending problems. The Reissner's plate bending theory is employed. Unlike the conventional direct or indirect formulations, the proposed integral equation is based on minimizing the relevant energy functional. In doing so, variational methods are used. A collocation based series, similar to the one used in the indirect discrete boundary element method, is used to remove domain integrals. Hence, a fully boundary integral equation is formulated. The main advantage of the proposed formulation is production of a symmetric stiffness matrix similar to that obtained in the finite element method. Numerical examples are presented to demonstrate the accuracy and the validity of the proposed formulation.

Isogeometric boundary integral formulation for Reissner’s plate problems

“…The curved plate bridge in Naga and Rashed (2013a), shown in Figure 41, is another example considered to demonstrate the advantages and the capabilities of the present formulation in dealing with irregular geometries without any boundary mesh generation and to compare the results obtained from the present formulation with the results of a problem from the literature. The plate (having a thickness equals 0.3 m) is fixed at Segments 1 and 3 and free at Segments 2 and 4.…”

“…Two IG-BEM models were solved to compare their results with the results of Q-BEM and the variational boundary element method (V-BEM) presented in Naga and Rashed (2013a) and to demonstrate the rate of convergence of the results obtained from the present formulation: Model A : Present IG-BEM using 20 knot intervals to represent the plate (p = 2), as shown in Figure 42, Model B : Present IG-BEM using 32 knot intervals to represent the plate (p = 2), as shown in Figure 42, …”