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• W2041439770 abstract "This paper presents a weighted p -version least squares finite element formulation (LSFEF) for two-dimensional plane elasto-statics and its application for simulating linear static behavior of laminated composites. The second order partial differential equations of equilibrium in displacements are recast into a series of first order coupled partial differential equations using stresses as auxiliary variables. The primary (displacements: u and v ) and the secondary (stresses: σ xx , τ xy and σ yy ) variables are interpolated using equal order, C 0 continuity, p -version hierarchical approximation functions. The p -version hierarchical approximation functions and the corresponding nodal variable operators are derived directly from the Lagrange family of interpolation functions by first constructing the one dimensional p -version hierarchical approximation functions and the corresponding nodal variable operators for three node equivalent configurations in the ξ and η directions and then taking their products. The least squares procedure yields a system of linear, symmetric simultaneous algebraic equations. The formulation provides inter-element continuity of displacements as well as stresses. Even though the element approximation is of type C 0 , in the limit when the error functional I converges to zero (i.e., when I → 0) the formulation behaves more like a C 1 type. In addition, for an inadequate mesh with an inadequate order of approximation for the elements, the element error functional values provide a mechanism for h and/or p -adaptive refinements. This is a unique feature of the LSFEF as compared to variational based formulations. Many other unique features of the formulation are discussed and illustrated in the paper. A numerical example is presented to illustrate the effectiveness of the formulation in simulating accurate inter-lamina stress behavior as well as accurate stress values and stress gradients at and near singularities. The results obtrained from the present formulation are compared with the results obtained from the p - version variational formulation and with those reported in the literature." @default.
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• W2041439770 date "1994-11-01" @default.
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• W2041439770 title "A least squares finite element formulation for plane elasto-statics based on p-version with applications to laminated composites" @default.
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• W2041439770 doi "https://doi.org/10.1016/0045-7949(94)90096-5" @default.
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