ШЕСТНАДЦАТИУЗЛОВОЙ ЭЛЕМЕНТ ОБОЛОЧКИ С МАТРИЧНОЙ СХЕМОЙ СТАБИЛИЗАЦИИ

Abstract

A sixteen-node finite element of a thin-walled shell is designed using a matrix stabilization scheme based on the introduction of the Hellinger-Reisner functional with independent deformation. Initially, the assumed independent deformation is divided into a lower order part and a higher order part. The stiffness matrix corresponding to the lower order assumed deformation is equivalent to the finite element stiffness matrix of the assumed displacement model with a reduced integration scheme. Spurious kinematic modes of the finite element are suppressed by introducing a stabilization matrix associated with a correctly selected set of assumed higher order deformation fields. As an example, a cylindrical shell with given geometric parameters and elasticity characteristics (elastic modulus, Poisson's ratio), loaded with concentrated forces at two opposite points, was considered. The problem considered fixed boundary conditions. Due to the symmetry of the geometry and load, only one octant of the shell was modeled with various finite element meshes, including irregular ones. The table showed the dimensionless deflections of the shell with fixed ends at the point where the concentrated force is applied. Good convergence is observed when the mesh of the finite element model is refined. There is no rigorous analytical solution for the presented case with fixed ends. The computational results show that this finite element can be used to provide reliable solutions for calculating the stress state of thin plates and shells irrespective of the curved geometry of the element, loading method and pinched boundary conditions. The presented element can be used to solve various modelling problems, as well as to test the performance of other shell elements.