Abstract
A new membrane finite element with four nodes that is based on the strain approach using Airy’s function is developed for the resolution of plane linear elasticity problems in general. The adoption of linear variations for the normal components of the strain and constant shear strain improves the accuracy of the elements. However, any singularity is eliminated by the use of a local reference frame oriented in an optimal manner. From numerical examples of a beam subjected to bending and shearing, we conclude that exact solutions can be obtained and they demonstrate the accuracy of the proposed procedure.
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