Spline super-element and its application in large deformation analysis.

摘要

In order to overcome the element shape effect induced problem-solving difficulties that have been frequently encountered in large deformation finite element analyses, especially in rubber and rubber-like material analyses, a special type of finite element—two-dimensional displacement and pressure hybrid spline super-element, has been formulated and implemented in the contest of geometric nonlinear theories and the theories of linear elasticity and hyperelasticity. The element's abilities of surviving severe distortions and stabilizing solution processes have been tested and demonstrated by several typical numerical experiments and application examples.; Spline interpolations are used in the element interpolations. The element can potentially have unlimited number of nodes, while the polynomials employed in the element interpolations are kept in a desired order. With a fairly high order and sufficient amounts of degrees of freedom, the element is capable of representing very complex deformations within the element. A non-interpolating method and its modifications have been introduced in the construction of the assumed pressure stress field within the element. With these methods, the pressure oscillations that usually caused by the inappropriate combination of displacement and pressure interpolations have been here effectively suppressed.; The spline super-element has two unique features. The first is its shape insensitivity, they can sustain severe distortions without causing significant solution degradations and problem solving difficulties, the second is that the element can be made in a substantially large size, a single element can coyer an entire area of interest, and a smoothly changed deformation gradient field can then be achieved within the area. Numerical experiments have showed that the deformation gradient field smoothness can significantly reduce the occurrence of non-physical deformations.; Potential future corks that could lead to a more effective spline super-element that can be used in nearly incompressible behavior analyses have also been discussed.