By Felippa C.
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Extra info for Advanced finite element methods
Out of print. M. M. Vainberg, Variational Methods for the Study of Nonlinear Operators, Holden-Day, 1964. An advanced monograph highly touted when it appeared since it was one of the first books covering nonlinear variational operators and the Newton-Kantorovich solution method. Requires good command of functional analysis, else forget it. Translated from Russian, but the job was not well done. Out of print. K. Washizu, Variational Methods in Elasticity and Plasticity, Pergamon Press, 1972 (2nd expanded edition 1981).
L Hints: The integral 0 whereas the integral 0 (M w δκ + M κ δw ) d x is the variation of L −M κ δκ d x is the variation of − 12 L 0 M w κ d x (work it out, it is a bit tricky) M κ κ d x. 2. 3 [A:30] The most general mixed functional in elasticity is called the Veubeke-Hu-Washizu or VHW functional. The three internal fields: displacements w, curvatures κ and moments M, are selected as masters and independently varied to get L L 1 Mκκ 2 [w, κ, M] = + M(κ w − κ) d x − 0 ˆ w qw d x − Mθ 0 B − Vˆ w .
1. Introduction We move now from the easy ride of Poisson problems and Bernoulli-Euler beams to the tougher road of elasticity in three dimensions. This Chapter summarizes the governing equations of linear elastostatics. Various notational systems are covered in sufficient detail to help readers with the literature of the subject, which is enormous and spans over two centuries. The governing equations are displayed in a Strong Form Tonti diagram. 1. A linear-elastic body of volume V in static equilibrium.
Advanced finite element methods by Felippa C.