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Locking-free compressible quadrilateral finite elements: Poisson’s ratio-dependent vector interpolants

Gautam Dasgupta
Organization: Columbia University
Department: Department of Civil Engineering and Engineering Mechanics
Journal / Anthology

Acta Mechanica
Year: 2014
Volume: 225
Issue: 1
Page range: 309-330

In any high-quality viscoplastic calculation, the objectivity related to shape and constitutive parameter indifference is desirable, especially when a continuous deformation into concavity is tracked. In the physical x−y frame, quadratic displacement vectors—explicitly coupled via Poisson’s ratio—encompass bar and Euler–Bernoulli beam modes. Analytically, the unique set of shape functions yields nodal loads and the element stiffness matrix from its area and the first and second area moments. Closed-form Mathematica results exhibit full compliance with all requirements of Iron’s patch tests.

*Engineering > Mechanical and Structural Engineering