Development of efficient finite elements from field consistence approach

In developing finite elements, the introduction of interpolation functions is the key step in properly converting a domain continuous field into a number of piecewise continuous ones. According to the research work reported in [16,17,18], for a multi-field problem, improperly selected interpolation functions, which ignore the coupling relations between the original field functions, might introduce in the element problems such as various lockings and slow convergence. To solve this problem, an alternative way with the name of field consistence approach for constructing efficient interpolation functions in multi-field elements are suggested in [16,17,18,12,13]. The main idea of the field consistence approach is to construct element interpolation functions from the (qausi-) general solutions to the corresponding Euler-Lagrangian equations. The symbolic operations involved in the approach are quite complex even for the simple 2-node Timoshenko beam element and a symbolic computational software is extremely needed in implementing the approach.