ON THE NONLINEAR ANALYSIS OF THIN SHELLS BY THE GENERALIZED MOVING-LEAST SQUARES APPROXIMATION

In the present contribution a geometrically exact thin shells formulation is presented. An analysis pro-cedure based on a meshfree approximation is outlined. As no restrictions are imposed on the rotational fields, the present formulation falls on the category of the geometrically exact structural theories. The derivation is made by imposing the kinematic hypoth-esis on the three-dimensional continuum. Contrary to previously presented works [1,2], where shear deformation was accounted, here only the bending deformation is included. We define energetically conjugated cross sectional stresses and strains based on the first Piola-Kirchhoff stress tensor and the deformation gradient, respectively. The complete linearization of the weak form is presented. For hyperelastic materials and conservative loadings the tangent bilinear form, i. e., the generalized stiffness matrix, is always symmetric even in points far from the generalized equilibrium positions. Initially curved shells are regarded as a stress-free deformed state from a chosen plane reference con-figuration [3]. The mapping between both configurations allows the exact consideration of the initial configuration