On geometrically nonlinear contact problems with friction

Rothert, H.; Idelberger, H.; Jacobi, William J.; Niemann, L.

doi:10.1016/0045-7825(85)90031-3

Cited by 13 publications

References 10 publications

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A consistent tangent stiffness matrix for three‐dimensional non‐linear contact analysis

Parisch

1989

Numerical Meth Engineering

116

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SUMMARYA consistent tangent stiffness matrix for the analysis of non-linear contact problems is presented. The associated element has three or four nodes and establishes contact between three-dimensional structures like solids and shells, It accounts for the non-linear kinematics of large deformation analysis and guarantees a quadratic Convergence rate. Two formulations, the penalty method and the Lagrange multiplier method, are investigated.

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A consistent tangent stiffness matrix for three‐dimensional non‐linear contact analysis

Parisch

1989

Numerical Meth Engineering

116

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A computational procedure for flexible beams with frictional contact constraints

Sun

Natori

Park

1993

Numerical Meth Engineering

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SUMMARYThis paper deals with the application of a parametric quadratic programming (PQP) I N T R O D U C T I O NWith the introduction of stronger, light weight and flexible synthetic materials the geometrically non-linear analysis of frames, buildings, many machine parts and structural components has become essential. In some engineering applications, these flexible structures will undergo frictional contacts. This adds another type of non-linearity. Owing to the highly non-lincar behaviour and the complex geometry of such structural components, detailed analysis of their structural behaviour requires efficient, robust and above all reliable numerical solvers. The aim of this paper is to offer the formulation and numerical solution of a class of geometrically non-linear beam structures subjected to frictional contact constraints.The most common methods of treating geometrically non-linear contact problems are based o n either the Lagrange multiplier method or on the penalty function method. When the former is employed. the conditions are enforced by augmenting the Lagrangian multipliers as additional system variables. However, this engenders computational difficulties as the resulting solution matrix contains zero diagonal terms corresponding to the Lagrange multipliers, in addition to the increased numbcr of unknowns as the Lagrange multipliers are part of the unknown solution vector.

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An effective two‐dimensional frictional contact model for arbitrary curved geometry

Saleeb

Chen

Chang

1994

Numerical Meth Engineering

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On geometrically nonlinear contact problems with friction

Cited by 13 publications

References 10 publications

A consistent tangent stiffness matrix for three‐dimensional non‐linear contact analysis

A consistent tangent stiffness matrix for three‐dimensional non‐linear contact analysis

A computational procedure for flexible beams with frictional contact constraints

An effective two‐dimensional frictional contact model for arbitrary curved geometry

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