![]() ![]() ![]() What Is The Method Of Weighted Residuals, I.e., Galerkin’s Method? Numerous articles and texts have been published, and new applications appear routinely in the literature.ģ. Since these early works, rapid growth in usage of the method has continued since the mid 1970s. However, others soon recognized the versatility of the method and its underlying rich mathematical basis for application in non-structural areas. The early use of finite elements lay in the application to structural-related problems. Actual coining of the term “finite element”appeared in a paper by Clough in 1960. ![]() Beginning in the mid 1950s,efforts to solve continuum problems in elasticity using small, discrete “elements” to describe the overall behavior of simple elastic bars began to appear, and such techniques were initially applied to the aircraft industry. The beginnings of the finite element method actually stem from these early numerical methods and the frustration associated with attempting to use finite difference methods on more difficult, geometrically irregular problems. The solution domain is discretized into individual elements – these elements are operated upon individually and then solved globally using matrix solution techniques.Įarly work on numerical solution of boundary-valued problems can be traced to the use of finite difference schemes South well used such methods in his book published in the mid 1940’s. The FEM has been used to solve a wide range of problems, and permits physical domains to be modeled directly using unstructured meshes typically based upon triangles or quadrilaterals in 2-D and tetrahedrons or hexahedrals in 3-D. The FEM utilizes the method of weighted residuals and integration by parts (Green-Gauss Theorem) to reduce second order derivatives to first order terms. The method is based on the integration of the terms in the equation to be solved, in lieu of point discretization schemes like the finite difference method. The FEM is a novel numerical method used to solve ordinary and partial differential equations. ![]()
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