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| A novel formulation of discontinuous deformation analysis enlightened by virtual element method |
| JIANG Wei1，2，XU Jiancheng1，WANG Lehua1，LIU Lipeng2，ZHENG Hong3 |
| (1. Key Laboratory of Geological Hazards on Three Gorges Reservoir Area，Ministry of Education，China Three Gorges University，Yichang，Hubei 443002，China；2. State Key Laboratory of Simulation and Regulation of Water Cycle in River Basin，China Institute of Water Resources and Hydropower Research，Beijing 100038，China；3. College of Architecture and Civil Engineering，Beijing University of Technology，Beijing 100124，China) |
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Abstract Vertex displacement-based discontinuous deformation analysis(DDA) was recently proposed to avoid the demerits caused by the original degree of freedom in DDA，but the current formulations developed by using the shape functions in polygonal finite element method have an unacceptable computational efficiency. To remedy this issue，a new formulation of DDA，utilizing VEM to define an individual displacement space and to calculate the potential energy for a block，and adopting original DDA to detect and analyze the contacts between blocks，is developed. The matrix expression for the block potential energy is mathematically deduced，and then the global equilibrium equations of the block system are derived based on the principle of minimum potential energy. A sliding block model is employed to determine the values of the multipliers in the approximations of the elastic deformation energy and the inertial force energy. The validity and computational efficiency of the new formulation are testified by three examples. Results show that the new formulation is capable to restrain the false volume expansion when simulating large rotation and to ensure the precision of the contact analysis. Most of all，the new formulation has a higher computational efficiency than the existing formulations of vertex displacement-based DDA.
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2022, Vol. 41 
