Area wise application of contact constraints in reduced mechanical systems Wolfgang Witteveen, University of applied sciences - Wels, Stelzhammerstr. 69, 4600 Wels, Austria, Phone: +43 (0) 7242 72811 3260, wolfgang.witteveen@fh-wels.at Nomenclature n number of DOF of FE model x nodel DOF vector of FE model Bf external forces acting on FE model K stiffness matrix of FE model nB number of boundary DOF Bx vector of boundary DOF nIJ number of joint DOF IJ x vector of joint DOF m number of master surface DOF IJ,M x vector of master surface DOF s number of slave surface DOF IJ,S x vector of slave surface DOF g number of master surface FE nodes g vector of relative joint normal displacement a vector of master surface FE node related areas r number of Ritz vectors ĭ reduction matrix red K reduced stiffness matrix red f reduced force vector q generalized coordinate ig i-th constraint equation based on x red ig i-th constraint equation based on q Q transformation matrix mi number of master surface DOF in subarea number i IJ,M,i x vector of master surface DOF of subarea number i gi number of master surface FE nodes in subarea number i ig vector of relative joint normal displacements of subarea number i ia vector of master surface FE node related areas in subarea number i * ig averaged penetration of subarea i e relative Error 1. Abstract Solid joint contact is characterized by nonlinear contact forces inside the joint. In case of gaping no contact forces are acting on the involved surfaces while penetration is avoided by the application of proper contact forces. In the common Finite Element (FE) method such forces are typically applied at nodal degree of freedom (DOF) inside the joint. This can be done using unilateral constraint equations or nonlinear penalty stiffness’s. In the frame work of modally reduced jointed structures just the penalty stiffness approach can be directly applied. In that case, the contact forces are computed based on the joint state and projected into the modal space. The problem is reduced to the question whether the mode base is capable to describe the relative displacements of the involved joint surfaces. This paper is a contribution to the more challenging problem when the contact is implemented using unilateral constraint equation will be higher than the number considered modes (DOF) which leads to on over constraint system. In order to overcome that problem an area wise application of the unilateral constraint equations is suggested instead of the common node wise one. After an introduction the presented idea will be outlined followed by a static example. The contribution ends with a discussion of the result and some conclusions. T. Proulx (ed.), Linking Models and Experiments, Volume 2, Conference Proceedings of the Society for Experimental Mechanics Series 5, 29 constraint equations. In that case the FE approach will not work in general because the number of nodal DOI 10.1007/978-1-4419-9305-2_3, © The Society for Experimental Mechanics, Inc. 2011
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