Singular boundary method for 2D dynamic poroelastic problems |
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| Institution: | 1. State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, International Center for Simulation Software in Engineering and Sciences, College of Mechanics and Materials, Hohai University, Nanjing 210098, China;2. School of Engineering, University of Mississippi, University, MS 38677, USA;1. State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, Center for Numerical Simulation Software in Engineering and Sciences, College of Mechanics and Materials, Hohai University, Nanjing 210098, China;2. School of Engineering, University of Mississippi, MS 38677, USA;3. College of Civil Engineering and Architecture, East China Jiaotong University, Nanchang 330013, China;4. Physics and Electronic Information College, Inner Mongolia University for Nationalities, Tongliao 028000, China;1. College of Mechanics and Materials, Hohai University, Nanjing, PR China;2. Department of Mathematics, University of Southern Mississippi, USA;1. State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, College of Mechanics and Materials, Hohai University, Nanjing 210098, China;2. College of Civil Engineering and Architecture, East China Jiaotong University, Nanchang 330013, China |
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| Abstract: | This paper extends a strong-form meshless boundary collocation method, named the singular boundary method (SBM), for the solution of dynamic poroelastic problems in the frequency domain, which is governed by Biot equations in the form of mixed displacement–pressure formulation. The solutions to problems are represented by using the fundamental solutions of the governing equations in the SBM formulations. To isolate the singularities of the fundamental solutions, the SBM uses the concept of the origin intensity factors to allow the source points to be placed on the physical boundary coinciding with collocation points, which avoids the auxiliary boundary issue of the method of fundamental solutions (MFS). Combining with the origin intensity factors of Laplace and plane strain elastostatic problems, this study derives the SBM formulations for poroelastic problems. Five examples for 2D poroelastic problems are examined to demonstrate the efficiency and accuracy of the present method. In particular, we test the SBM to the multiply connected domain problem, the multilayer problem and the poroelastic problem with corner stress singularities, which are all under varied ranges of frequencies. |
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| Keywords: | Singular boundary method Meshless boundary collocation method Porous media Biot equations Fundamental solutions |
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