This paper discusses the application of the boundary contour method fo r resolving plate bending problems. The exploitation of the integrand divergence free property of the plate bending boundary integral equation bas...This paper discusses the application of the boundary contour method fo r resolving plate bending problems. The exploitation of the integrand divergence free property of the plate bending boundary integral equation based on the Kirc hhoff hypothesis and a very useful application of Stokes' Theorem are presented to convert surface integrals on boundary elements to the computation of bending potential functions on the discretized boundary points,even for curved surface elements of arbitrary shape. Singularity and treatment of the discontinued corne r point are not needed at all. The evaluation of the physics variant at internal points is also shown in this article. Numerical results are presented for some plate bending problems and compared against analytical and previous solutions.展开更多
Equivalent Boundary Integral Equations (EBIE) with indirect unknowns for thin elastic plate bending theory, which is equivalent to the original boundary value problem, is established rigorously by mathematical techniq...Equivalent Boundary Integral Equations (EBIE) with indirect unknowns for thin elastic plate bending theory, which is equivalent to the original boundary value problem, is established rigorously by mathematical technique of non-analytic continuation and is fully proved by means of the variational principle. The previous three kinds of boundary integral equations with indirect unknowns are discussed thoroughly and it is shown that all previous results are not EBIE.展开更多
In this paper, the p- version of the finite element method of lines (FEMOL) for the analysis of the Mindlin-Reissner plate bending problems is presented and a class of p-FEMOL elements with polynomial degrees as high ...In this paper, the p- version of the finite element method of lines (FEMOL) for the analysis of the Mindlin-Reissner plate bending problems is presented and a class of p-FEMOL elements with polynomial degrees as high as nine is developed. Numerical examples given in this paper show tremendous performance of the present method: namely, rapid convergence rate, high accuracy for both displacements and stress resultants, removal of shear-locking trouble, capability of dealing with difficult problems such as the boundary layer behavior near a free edge and stress concentration around a hole.展开更多
文摘This paper discusses the application of the boundary contour method fo r resolving plate bending problems. The exploitation of the integrand divergence free property of the plate bending boundary integral equation based on the Kirc hhoff hypothesis and a very useful application of Stokes' Theorem are presented to convert surface integrals on boundary elements to the computation of bending potential functions on the discretized boundary points,even for curved surface elements of arbitrary shape. Singularity and treatment of the discontinued corne r point are not needed at all. The evaluation of the physics variant at internal points is also shown in this article. Numerical results are presented for some plate bending problems and compared against analytical and previous solutions.
文摘Equivalent Boundary Integral Equations (EBIE) with indirect unknowns for thin elastic plate bending theory, which is equivalent to the original boundary value problem, is established rigorously by mathematical technique of non-analytic continuation and is fully proved by means of the variational principle. The previous three kinds of boundary integral equations with indirect unknowns are discussed thoroughly and it is shown that all previous results are not EBIE.
文摘In this paper, the p- version of the finite element method of lines (FEMOL) for the analysis of the Mindlin-Reissner plate bending problems is presented and a class of p-FEMOL elements with polynomial degrees as high as nine is developed. Numerical examples given in this paper show tremendous performance of the present method: namely, rapid convergence rate, high accuracy for both displacements and stress resultants, removal of shear-locking trouble, capability of dealing with difficult problems such as the boundary layer behavior near a free edge and stress concentration around a hole.
