摘要
针对正交各向异性位势问题,提出了Trefftz有限元解法。通过坐标变换和拉普拉斯方程特征函数,求得正交各向异性问题的完备解系,进而构建单元域内位势场。然后,基于杂交泛函,结合单元网线位势场,系统推导了相应的Trefftz有限元列式。文末给出两个数值算例,使用四节点四边形单元OPT44建立有限元模型,计算结果验证了本文方法的有效性和准确性。
This paper presents the Trefftz finite element analysis of orthotropic potential problems. The complete set of homogeneous solutions to orthotropic potential problem, which is employed to construct intra-element potential field, has been obtained using coordinate transformation and eigenfunctions of La- place equation. In combination with element frame potential field, the corresponding Trefftz finite ele- ment formulation is systematically derived based on the hybrid functional. Finally, two numerical exam- ples, which are modeled using four-node quadrilateral elements OPT44, are investigated. And the results demonstrate the effectivity and accuracy of proposed approach.
出处
《力学季刊》
CSCD
北大核心
2012年第3期499-506,共8页
Chinese Quarterly of Mechanics
基金
上海高校选拔培养优秀青年教师科研专项基金(GJD10019)
上海市教委重点攻关项目(10ZZ124)
