Abstract
An approach is presented for solving plate bending problems using a high-order infinite element method (IEM) based on Mindlin–Reissner plate theory. In the proposed approach, the computational domain is partitioned into multiple layers of geometrically similar virtual elements which use only the data of the boundary nodes. Based on the similarity, a reduction process is developed to eliminate virtual elements and overcome the problem that the conventional reduction process cannot be directly applied. Several examples of plate bending problems with complicated geometries are reported to illustrate the applicability of the proposed approach and the results are compared with those obtained using ABAQUS software. Finally, the bending behavior of a rectangular plate with a central crack is analyzed to demonstrate that the stress intensity factor (SIF) obtained using the high-order PIEM converges faster and closer than low-order PIEM to the analytical solution.
Highlights
In the past years, meshless methods have been used [3, 4] as alternatives to the finite element method (FEM)
A new reduction process has been developed to eliminate virtual elements in the infinite element method (IEM) domain so that the infinite element (IE) range is condensed and transformed to form a super element with the master nodes on the boundary only
We present a high-order PIEM based on Mindlin–Reissner plate theory
Summary
Mindlin–Reissner plate theory is an extension of Kirchhoff–Love plate theory, which considers shear deformations through the thickness of a plate. Θx and θy are the rotations of the midplane about the y and x axes, respectively; and c is the angle caused by transverse shear deformation. Executing a transformation from physical to natural coordinates yields the rotation and transverse displacements as follows:. I 1 where Hi represents the n-node plate finite element shape function and (ζ, η) represents the natural coordinates. E nine-node-plate finite element stiffness matrix can be derived using Mindlin–Reissner theory and by transforming z, w. E associated plate stiffness is expressed in equation (5), where [KB] and [KS] denote the bending stiffness and shear stiffness, respectively. Zη zη [BB] and [BS] comprise shape functions, as presented in equations (8) and (9), respectively.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
