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• W2076210642 endingPage "3037" @default.
• W2076210642 startingPage "3007" @default.
• W2076210642 abstract "A formulation for the plane 4-node quadrilateral finite element is developed based on the principle of virtual displacements for a deformable body. Incompatible modes are added to the standard displacement field. Then expressions for gradient operators are obtained from an expansion of the basis functions into a second-order Taylor series in the physical co-ordinates. The internal degrees of freedom of the incompatible modes are eliminated on the element level. A modified change of variables is used to integrate the element matrices. For a linear elastic material, the element stiffness matrix can be separated into two parts. These are equivalent to a stiffness matrix obtained from underintegration and a stabilization matrix. The formulation includes the cases of plane stress and plane strain as well as the analysis of incompressible materials. Further, the approach is suitable for non-linear analysis. There, an application is given for the calculation of inelastic problems in physically non-linear elasticity. The element is efficient to implement and it is frame invariant. Locking effects and zero-energy modes are avoided as well as singularities of the stiffness matrix due to geometric distortion. A high accuracy is obtained for numerical solutions in displacements and stresses." @default.
• W2076210642 created "2016-06-24" @default.
• W2076210642 creator A5016987095 @default.
• W2076210642 creator A5025052204 @default.
• W2076210642 date "1995-09-30" @default.
• W2076210642 modified "2023-10-06" @default.
• W2076210642 title "A formulation for the 4-node quadrilateral element" @default.
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• W2076210642 doi "https://doi.org/10.1002/nme.1620381802" @default.
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