A Novel Approach in Formulation of Special Finite Elements

这项研究包括一种新的方法，以发展更准确和有效的技术来解决具有不连续性和局部非线性的三维问题。有限元方法的重要意义在于它具有处理任意几何形状和不同材料性质的潜力。可以构造包含单元公式中的不连续性的特殊有限元，并将该特殊单元耦合到模拟系统其余部分的网格。与其他元素公式不同，这种特殊的元素公式将把已有的经典解合并到元素公式中。例如，对于结构问题，在近似中使用的位移函数将完全满足分析结果。这将通过在单元刚度系数的推导中引用经典解作为约束来实现。这项研究将带来一种新的技术，在不需要网格细化的情况下，在局部级别处理不连续的局部几何-材料非线性。为了进行数字比较，将开发一个计算机程序。

The research includes a new approach to develop more accurate and efficient techniques for solution of three dimensional problems with discontinuities and local nonlinearities. The finite element method owes its significance to its potentiality for the treatment of rather arbitrary geometry, and different material properties. One may build a special finite element that contains the discontinuity in the element formulation, and couple the special element to the mesh that models the rest of the system. The special element formulation, unlike others, will incorporate already existing classical solutions into the element formulations. The displacement function, for structural problems for example, used in approximations will exactly satisfy the analytical results wherever available. This will be achieved by invoking the classical solutions as constraints in the derivation of element stiffness coefficients. This research will bring about a new technique to handle discontinuities, local geometric-material nonlinearities at local level without requiring mesh refinements. For numerical comparison purposes a computer program will be developed.