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The DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Thu, 29 Feb 2024 11:28:03 GMT2024-02-29T11:28:03ZA finite element/quaternion/asymptotic numerical method for the 3D simulation of flexible cables
http://hdl.handle.net/10985/11412
A finite element/quaternion/asymptotic numerical method for the 3D simulation of flexible cables
COTTANCEAU, Emmanuel; THOMAS, Olivier; VERON, Philippe; ALOCHET, Marc; DELIGNY, Renaud
A flexible cable is modeled by a geometrically exact beam model with 3D rotations described using quaternion parameters. The boundary value problem is then discretized by the finite element method. The use of an asymptotic numerical method to solve the problem, quadratic equations, is well suited to the quaternion parametrization. This combination of methods leads to a fast, robust and accurate algorithm very well-adapted for the simulation of the assembly process of cables. This is proved by running many examples involving complicated solutions.
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10985/114122016-01-01T00:00:00ZCOTTANCEAU, EmmanuelTHOMAS, OlivierVERON, PhilippeALOCHET, MarcDELIGNY, RenaudA flexible cable is modeled by a geometrically exact beam model with 3D rotations described using quaternion parameters. The boundary value problem is then discretized by the finite element method. The use of an asymptotic numerical method to solve the problem, quadratic equations, is well suited to the quaternion parametrization. This combination of methods leads to a fast, robust and accurate algorithm very well-adapted for the simulation of the assembly process of cables. This is proved by running many examples involving complicated solutions.A finite element/quaternion/asymptotic numerical method for the 3D simulation of flexible cables
http://hdl.handle.net/10985/14335
A finite element/quaternion/asymptotic numerical method for the 3D simulation of flexible cables
COTTANCEAU, Emmanuel; THOMAS, Olivier; VERON, Philippe; ALOCHET, Marc; DELIGNY, Renaud
In this paper, a method for the quasi-static simulation of flexible cables assembly in the context of automotive industry is presented. The cables geometry and behavior encourage to employ a geometrically exact beam model. The 3D kinematics is then based on the position of the centerline and on the orientation of the cross-sections, which is here represented by rotational quaternions. Their algebraic nature leads to a polynomial form of equilibrium equations. The continuous equations obtained are then discretized by the finite element method and easily recast under quadratic form by introducing additional slave variables. The asymptotic numerical method, a powerful solver for systems of quadratic equations, is then employed for the continuation of the branches of solution. The originality of this paper stands in the combination of all these methods which leads to a fast and accurate tool for the assembly process of cables. This is proved by running several classical validation tests and an industry-like example.
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10985/143352018-01-01T00:00:00ZCOTTANCEAU, EmmanuelTHOMAS, OlivierVERON, PhilippeALOCHET, MarcDELIGNY, RenaudIn this paper, a method for the quasi-static simulation of flexible cables assembly in the context of automotive industry is presented. The cables geometry and behavior encourage to employ a geometrically exact beam model. The 3D kinematics is then based on the position of the centerline and on the orientation of the cross-sections, which is here represented by rotational quaternions. Their algebraic nature leads to a polynomial form of equilibrium equations. The continuous equations obtained are then discretized by the finite element method and easily recast under quadratic form by introducing additional slave variables. The asymptotic numerical method, a powerful solver for systems of quadratic equations, is then employed for the continuation of the branches of solution. The originality of this paper stands in the combination of all these methods which leads to a fast and accurate tool for the assembly process of cables. This is proved by running several classical validation tests and an industry-like example.A finite element/quaternion/asymptotic numerical method for the 3D simulation of flexible cables
http://hdl.handle.net/10985/15357
A finite element/quaternion/asymptotic numerical method for the 3D simulation of flexible cables
COTTANCEAU, Emmanuel; THOMAS, Olivier; VÉRON, Philippe; ALOCHET, Marc; DELIGNY, Renaud
In this paper, a method for the quasi-static simulation of flexible cables assembly in the context of automotive industry is presented. The cables geometry and behavior encourage to employ a geometrically exact beam model. The 3D kinematics is then based on the position of the centerline and on the orientation of the cross-sections, which is here represented by rotational quaternions. Their algebraic nature leads to a polynomial form of equilibrium equations. The continuous equations obtained are then discretized by the finite element method and easily recast under quadratic form by introducing additional slave variables. The asymptotic numerical method, a powerful solver for systems of quadratic equations, is then employed for the continuation of the branches of solution. The originality of this paper stands in the combination of all these methods which leads to a fast and accurate tool for the assembly process of cables. This is proved by running several classical validation tests and an industry-like example.
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10985/153572018-01-01T00:00:00ZCOTTANCEAU, EmmanuelTHOMAS, OlivierVÉRON, PhilippeALOCHET, MarcDELIGNY, RenaudIn this paper, a method for the quasi-static simulation of flexible cables assembly in the context of automotive industry is presented. The cables geometry and behavior encourage to employ a geometrically exact beam model. The 3D kinematics is then based on the position of the centerline and on the orientation of the cross-sections, which is here represented by rotational quaternions. Their algebraic nature leads to a polynomial form of equilibrium equations. The continuous equations obtained are then discretized by the finite element method and easily recast under quadratic form by introducing additional slave variables. The asymptotic numerical method, a powerful solver for systems of quadratic equations, is then employed for the continuation of the branches of solution. The originality of this paper stands in the combination of all these methods which leads to a fast and accurate tool for the assembly process of cables. This is proved by running several classical validation tests and an industry-like example.