Analysis Of Plates By The Weak Form Quadrature Element Method

The weak form quadrature element method (abbreviated as QEM) isregarded as a distinctive numerical method for combining numerical integrationand numerical differentiation in an element. After dividing the physical domaininto several integrable subdomains, numerical integration and numericaldifferentiation are used in the weak form description of a problem. The QEM ischaracterized by it mathematical discretization and the construction of shapefunctions is inferior to the selection of an efficient numerical integration scheme.Consequently, it is easy to form high-order elements. The present work aims at aseries of plate problems which requires C1continuity conditions:(1) Linear analysis of thin plate. Using Gauss-Lobatto integration, differentialquadrature method and generalized differential quadrature method, an arbitrarilyquadrilateral quadrature element which satisfies compatibility conditions ofdisplacements is formulated to deal with thin plate problems. As compared withthe finite element method, the QEM has shown significantly high efficiency. Atransformation technique is developed to make elements of different ordersmatch, improving the feasibility of the quadrature element for thin plates.(2) Linear analysis of high-order plates. The QEM is used to study Reddy’s andKant’s high-order plates. It is shown that the QEM can deal with high-orderplate problems which are characterized by complicated displacement fields. Theexamples has shown that the high-order plate models cannot deal with thickplates.(3) Geometrically nonlinear analysis of thin plate. Geometrically nonlinearanalysis has a continuous displacement field and often requires a highcomputational cost, demanding the use of efficient solution techniques. The vonKárman plate is studied using the QEM, demonstrating its high accuracy andefficiency. (4) Elasto-plastic analysis of thin plate. A high-order quadrature element forelasto-plastic analysis of thin plate is formulated. Numerical examples show thatthe QEM has powerful capability in elasto-plastic analysis and even limitanalysis of plates.The numerical examples has shown that the QEM is a reliable,high-performance method dealing with plate problems, and has enoughflexibility to use in the actual engineerings.