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针对水工结构中的局部接触问题,提出了一种新的数值分析方法—多体有限元法。基于DDA方法的分析思路,以结构面切割而成的块体作为分析单元,每一块体均可允许自身有独立的位移和变形,通过块体间的接触和几何关系形成一个完整的块体系统。块体内部采用有限元法求解,块体之间通过接触力相互联系,且在接触界面上引入变形协调条件,保证了多个块体互相接触作用时块体位移和应力状态的连续性,从而使得计算更加符合实际情况。该方法接触求解过程中无需指定法向刚度及切向刚度等参数,避免了DDA方法因引入刚性弹簧而出现的嵌入问题,同时提高了块体内部变形的求解精度。推导了多体有限元法求解接触问题的支配方程,并给出了其增量形式的定解条件和判定条件。最后通过3个数值算例验证了本文方法的正确性和有效性。
Aiming at the problem of local contact in hydraulic structure, a new numerical analysis method, multi-body finite element method, is proposed. Based on the analysis of DDA method, the blocks cut from the structural plane are used as the analysis unit. Each block can allow its own independent displacement and deformation. Through the contact and geometric relationship between blocks, a complete block system . The interior of the block is solved by the finite element method. The blocks are connected with each other by the contact force, and the deformation coordination condition is introduced at the contact interface to ensure the continuity of the block displacement and the stress state when multiple blocks contact with each other Make the calculation more in line with the actual situation. The method avoids the need of specifying parameters such as normal stiffness and tangential stiffness in the contact solving process, avoids the embedding problem caused by the introduction of a rigid spring in the DDA method, and improves the solution accuracy of the internal deformation of the block. The governing equations of multi-body finite element method for solving the contact problem are deduced, and the definitive solution conditions and the judgment conditions of the incremental form are given. Finally, numerical examples are given to verify the correctness and effectiveness of the proposed method.