RECENT ADVANCES IN THE METHOD OF WEIGHTED RESIDUALS ON SOLID MECHANICS IN CHINA

Abstract

Abstract: This paper presents a review of research work in recent years on the method of weighted residuals (MWR) on solid mechanics in the People’s Republic of China. MWR, as a kind of mathematical method by which approximate solutions of differential equations may be obtained, is being extensively used in the fields of fluid mechanics, heat transfer, etc. In China,prompted by needs, this method has been developed to be used on solid mechanics in recent years and has also been recognized as having merits over other methods.In this paper, after a brief description of MWR, a review of this method as applied in members, plates, shells, latticed shells, elasticity problems of two dimensions and three dimensions, research on its functional theory and theory of convergency, on positions of collocation points, selection of trial functions, the use of the spline function and beam functions, nonlinear problems and its application in time domains are given.Finally, the author, summarizing investigations in the past, suggests several future research directions for MWR which may be advantageous to the industrialization of China.

Key words: Φ-strongly accretive operator, Φ-strongly pseudo-contractive mapping, Ishikawa iterative sequence, Mann iterative sequence

Xu Ci-da. RECENT ADVANCES IN THE METHOD OF WEIGHTED RESIDUALS ON SOLID MECHANICS IN CHINA. Applied Mathematics and Mechanics (English Edition), 1982, 3(6): 793-800.

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