A class of mixed assumed strain methods and the method of incompatible modes

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<jats:title>Abstract</jats:title><jats:p>A three‐field mixed formulation in terms of displacements, stresses and an <jats:italic>enhanced strain</jats:italic> field is presented which encompasses, as a particular case, the classical method of incompatible modes. Within this frame‐work, incompatible elements arise as particular ‘compatible’ mixed approximations of the enhanced strain field. The conditions that the stress interpolation contain piece‐wise constant functions and be <jats:italic>L</jats:italic><jats:sub>2</jats:sub>‐ortho‐gonal 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 non‐linear analysis.</jats:p>

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