梁板壳有限单元中的各种闭锁现象及解决方法

对梁元和板壳单元中存在的各种闭锁现象进行详细的分析，对现有的一些解决方法的优劣性进行比较，以使人们对闭锁现象有更深入的认识，并能有效地消除或减轻它们的不利影响.分别在二维、三维梁元与板壳单元有限元公式中引入Hellinger-Reissner混合函数或降阶积分，以减轻或消除闭锁现象对单元计算精度的不利影响.通过4个算例来阐明闭锁现象随单元受力情况、单元厚度、单元网格划分的不同而对结构非线性分析结果所带来的不同程度的影响. 结果表明，闭锁现象对结构的数值分析结果影响显著，对以受弯为主而膜应力很小甚至为零的单元，膜闭锁现象非常严重，而对薄壁单元，剪切闭锁的影响特别严重；采用单元的混合公式或在协调元中采用降阶积分，可有效地消除单元的各种闭锁现象和插值函数的误差对单元计算精度带来的不利影响，能使单元计算精度和计算效率得到显著改善.

Strategies for overcoming locking phenomena in beam and shell finite element formulations

The locking phenomena existing in beam and shell finite element formulations were explained, and the advantages and disadvantages of several commonly used solution procedures were analyzed so that the effects of these locking problems can be solved properly. Mixed element formulations based on the Hellinger-Reissner function and the reduced integration procedure were adopted respectively to alleviate or eliminate the effects of locking phenomena on the computational accuracy and efficiency of beam and shell elements. Four examples were analyzed to illuminate the effects of locking phenomena on beam/shell structures with different loading cases, element meshes and element thickness. The effects of locking phenomena are serious. The membrane locking phenomenon is dominant especially for a bending element, while the effect of the shear locking phenomenon is significant for a thin-walled element. Adopting the Hellinger-Reissner mixed element formulation or introducing the reduced integration procedure in conforming element formulations can eliminate the effects of locking phenomena and interpolation function errors effectively and satisfy the computational accuracy and efficiency of elements.