Recent studies show that the unsymmetric finite element method exhibits excellent performance when the discretized meshes are severely distorted. In this article, a new unsymmetric 4‐noded quadrilateral plane element is presented using both incompatible test functions and trial functions. Five internal nodes, one at the elemental central and four at the middle sides, are added to ensure the quadratic completeness of the elemental displacement field. Thereafter, the total nine nodes are applied to form the shape functions of trial function, and the Lagrange interpolation functions are adopted as the incompatible test shape functions of the internal nodes. The incompatible test displacements are then revised to satisfy the patch test. Numerical tests show that the present element can provide very good numerical accuracy with badly distorted meshes. Unlike the existing unsymmetric four‐node plane elements in which the analytical stress fields are employed, the present element can be extended to boundary value problems of any differential equations with no difficulties.
SUMMARYA moving least squares di erential quadrature (MLSDQ) method is developed and employed for the analysis of moderately thick plates based on the ÿrst-order shear deformation theory (FSDT). To carry out the analysis, the governing equations in terms of the generalized displacements (transverse de ection and two rotations) of the plate are formulated by employing the moving least squares approximation. The weighting coe cients used in the MLSDQ approximation are computed through a fast computation of shape functions and their derivatives. Numerical examples illustrating the accuracy, stability and convergence of the MLSDQ method are presented. E ects of support size, order of completeness and node irregularity on the numerical accuracy are investigated.
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