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An entropy-based evaluation of contact forces in continuum mechanics of elastic structures.pdf

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Finite Elements in Analysis and Design 114 (2016) 78–84 Contents lists available at ScienceDirect Finite Elements in Analysis and Design journal homepage: /locate/?nel An entropy-based evaluation of contact forces in continuum mechanics of elastic structures Zhaocheng Xuan a,n, Panayiotis Papadopoulos b, Jianyu Li c, Lili Zhang a a Department of Computer Science, Tianjin University of Technology and Education, Tianjin 300222, China b Department of Mechanical Engineering, University of California, Berkeley, CA 94720-1740, USA c Department of Mechanical Engineering, Tianjin University of Science and Technology, Tianjin 300222, China article info Article history: Received 9 July 2015 Received in revised form 4 February 2016 Accepted 14 February 2016 Available online 3 March 2016 Keywords: Contact forces Entropy Ensemble Finite elements abstract The maximum entropy principle has proved to be a versatile tool for solving problems in many ?elds. In this paper, we extend entropy and its use in statistical physics to evaluate contact forces in the continuum mechanics of elastic structures. Each potential contact node of an elastic structure discretized by ?nite elements along with the normalized contact force on the node is considered as a system and all potential contact nodes together with their normalized contact forces are considered as a canonical ensemble, with the normalized contact force of each node representing the microstate of the node. The product of non-penetration conditions for potential contact nodes and the normalized nodal contact forces then act as an expectation that its value will be zero, and maximizing the entropy under the constraints of the expectation and the minimum potential energy principle results in an explicit probability distribution for the normalized contact forces that shows the relation between contact forces and displacements in a formulation similar to the formulation for particles occupying microstates in statistical physics. Moreove