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Corrugated membranes are extremely important structural parts of a great number of devices, highly sensitive pressure sensors in particular. In engineering of corrugated shapes different factors could be taken into account as crucial. Among them – membrane’s work without buckling, buckling for the prescribed load, flatness of the membrane characteristic – dependence of the applied pressure on the...
A unique derivation of quadrilateral shell elements with six degrees of freedom at each node is presented. The theoretical and numerical formulation is based on the combination of a membrane element with drilling degrees of freedom and a shear deformable plate element. The predictive quality and the computational efficiency is improved by applying multifield variational principles in connection with...
A non-standard approach is proposed to develop a simple and computationally effective triangular finite element applicable to geometrically nonlinear analysis of composite shells. The approach is based on the natural components of the stress and strain tensors and their invariants which allow one to express the strain energy of the shell in a compact form without coordinate transformations. The natural...
Some singular concepts and non-standard practices in the FEM solution of geometrically nonlinear shell problems are highlighted and discussed. In particular, four issues are addressed. (i) The question of the drilling rotation: a shell is essentially a non-polar medium in its tangent plane, so the drilling rotation is a redundant d.o.f. to be defined by an extra stress field, and the latter ought...
One way to develop theories for the elastic deformation of two- or one-dimensional structures (like, e.g., shells and beams) under a given load is the uniform-approximation technique (see [2] for an introduction). This technique derives lower-dimensional theories from the general three-dimensional boundary value problem of linear elasticity by the use of series-expansions. It leads to a set of power...
Enhanced four-node shell elements based on the Hu-Washizu (HW) functional are developed for the Green strain and constitutive laws modified by the zero-normal-stress condition. They have six dofs/node, i.e. the drilling rotation is included. The key features of the approach are as follows: 1. For the membrane part of HW shell elements, we use the 7-parameters stress, 9-parameter strain and 2-parameter...
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