Direct localized boundary-domain integro-differential formulations for physically nonlinear elasticity of inhomogeneous body |
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| Affiliation: | 1. Plasma Science and Fusion Center, MIT, 175 Albany St., Cambridge, MA 02139, USA;2. Fusion Research Center, University of Texas-Austin, Austin, TX 78712, USA;1. School of Aerospace, Mechanical and Mechatronic Engineering, J07, University of Sydney, NSW 2006, Australia;2. School of Engineering Systems, Queensland University of Technology, GPO Box 2434, Brisbane, QLD 4001, Australia;3. School of Mechanical & Aerospace Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798, Singapore;4. Department of Mechanical Engineering, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260, Singapore;1. Department of Civil Engineering, Zhejiang University, Hangzhou 310027, PR China;2. Department of Building and Construction, City University of Hong Kong, Kowloon, Hong Kong, PR China |
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| Abstract: | A static mixed boundary value problem (BVP) of physically nonlinear elasticity for a continuously inhomogeneous body is considered. Using the two-operator Green-Betti formula and the fundamental solution of an auxiliary linear operator, a non-standard boundary-domain integro-differential formulation of the problem is presented, with respect to the displacements and their gradients. Using a cut-off function approach, the corresponding localized parametrix is constructed to reduce the nonlinear BVP to a nonlinear localized boundary-domain integro-differential equation. Algorithms of mesh-based and mesh-less discretizations are presented resulting in sparsely populated systems of nonlinear algebraic equations. |
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