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A class of mixed assumed strain methods and the method of incompatible modes. (English) Zbl 0724.73222
Summary: A three-field mixed formulation in terms of displacements, stresses and an enhanced strain field is presented which encompasses, as a particular case, the classical method of incompatible modes. Within this framework, incompatible elements arise as particular ‘compatible’ mixed approximations of the enhanced strain field. The conditions that the stress interpolation contain piecewise constant functions and be ${L}_{2}$-orthogonal to the enhanced strain interpolation, ensure satisfaction of the patch test and allow the elimination of the stress field from the formulation. The preceding conditions are formulated in a form particularly convenient for element design. As an illustration of the methodology three new elements are developed and shown to exhibit good performance: a plane 3D elastic/plastic QUAD, an axisymmetric element and a thick plate bending QUAD. The formulation described herein is suitable for nonlinear analysis.

##### MSC:
 74S05 Finite element methods in solid mechanics 74S30 Other numerical methods in solid mechanics 74P10 Optimization of other properties (solid mechanics)