Triangular Quadrature Element Analysis Of Geometrically Exact Shells

Plates and shells are commonplace engineering structures with a significantly smaller scale in the thickness dimension.Due to their lightness and large spans,plates and shells are widely adopted in civil,aircraft,astronautic,mechanic and power engineering.Even under normal loads,shells are constantly under a compressive stress over the whole or partial cross section,thereby subject to a high level of buckling risk.Nevertheless,a large number of well-designed shell structures still possess a considerable residual capacity in the post-buckling stage.In the aftermath of earthquakes or other emergencies,if a large scale or global collapse can be avoided,then the time and space to evacuate and rescue can be expanded while the loss of life and value be reduced.Because of these needs a reliable post-buckling analysis is called for in a regime that conventional low-order finite elements lacks accuracy and efficiency.With the maturity of numerical methods and the explosion of computing power,high-order methods have made the tracking of complete buckling path more accessible.The weak-form quadrature element method is based on the discretized versions of various variational principles,embracing high-order numerical integrations from the beginning with differentiations adopted on the one and same nodal representation.It has advantages in domains of complex geometry,complicated boundary conditions,non-uniform loading.The geometrically exact shell theory provides an objective and accurate formulation of large displacements and large three-dimensional rotations in terms of the section and director kinematics.Basic postulations include an inextensible director vector orthogonal to the mid-plane,a linearly distributed strain along the director and two rotations according to Reissner-Mindlin plus a drilling degree of freedom about itself.In the local coordinate system,the deformations are quantified by the quaternion representations of 3D rotations.A minimal number of degrees of freedom are adopted in the actual computation.Based on the basic postulation of shear strains,two distinct shell models with different degrees of freedom(DOFs)are presented,one being the 3-DOFs Kirchhoff-Love thin shell,and the other being the 6-DOFs Reissner-Mindlin model with a drilling DOF.Numerical tests are carried out according to the model characteristics in order to verify the correctness of the procedure.In all,this thesis extends the potentially industrializable geometrically-exact shell models to the triangular quadrature element method,improves the techniques of defining DOFs and applying boundary conditions.This work also represents a starting point to the self-adaptive application of quadrature element methods to complex geometries.