Modelling, analysis, and numerical simulation of a spring-rods system with unilateral constraints
Copyright policy )Modelling, analysis, and numerical simulation of a spring-rods system with unilateral constraints
In this paper, we consider a mathematical model which describes the equilibrium of two elastic rods attached to a nonlinear spring. We derive the variational formulation of the model which is in the form of an elliptic quasivariational inequality for the displacement field. We prove the unique weak solvability of the problem, then we state and prove some convergence results, for which we provide the corresponding mechanical interpretation. Next, we turn to the numerical approximation of the problem based on a finite element scheme. We use a relaxation method to solve the discrete problems that we implement on the computer. Using this method, we provide numerical simulations which validate our convergence results.
- UMR 7013 Institut Denis Poisson France
- National Scientific and Technical Research Council Argentina
- University of Perpignan France
- Jagiellonian University Poland
- Austral University Argentina
Alternative medicine, Economics, 74K10, 74K05, 74M15, 74G35, 74G30, 74G15, 49J40, Kinematic and Dynamic Analysis of Robot Manipulators, Social psychology, SPRING-RODS SYSTEM, CONVERGENCE RESULT, Engineering, Displacement (psychology), Relaxation (psychology), Classical Analysis and ODEs (math.CA), Pathology, https://purl.org/becyt/ford/1.1, Psychology, Rod, DISCRETE SCHEME, Mathematical Physics, Variational inequality, WEAK SOLUTION, Physics, Mathematical optimization, Topology Optimization in Structural Engineering, Numerical Analysis (math.NA), Mathematical Physics (math-ph), Computational Contact Mechanics and Variational Inequalities, FOS: Philosophy, ethics and religion, FOS: Psychology, Stiffness Optimization, Computational Theory and Mathematics, Mathematics - Classical Analysis and ODEs, Physical Sciences, Calibration, Convergence (economics), Medicine, FINITE ELEMENT, Finite element method, Dynamic relaxation, FOS: Physical sciences, Geometry, Structural engineering, QUASIVARIATIONAL INEQUALITY, Epistemology, Spring (device), Mathematical analysis, Quantum mechanics, UNILATERAL CONSTRAINT, FOS: Mathematics, Mathematics - Numerical Analysis, https://purl.org/becyt/ford/1, Economic growth, Civil and Structural Engineering, Non-linear Elastic Structures, Scheme (mathematics), Applied mathematics, Philosophy, Nonlinear Dynamics, Control and Systems Engineering, Dynamic Modeling, Computer Science, Nonlinear system, Simple (philosophy), Psychotherapist, Mathematics
Alternative medicine, Economics, 74K10, 74K05, 74M15, 74G35, 74G30, 74G15, 49J40, Kinematic and Dynamic Analysis of Robot Manipulators, Social psychology, SPRING-RODS SYSTEM, CONVERGENCE RESULT, Engineering, Displacement (psychology), Relaxation (psychology), Classical Analysis and ODEs (math.CA), Pathology, https://purl.org/becyt/ford/1.1, Psychology, Rod, DISCRETE SCHEME, Mathematical Physics, Variational inequality, WEAK SOLUTION, Physics, Mathematical optimization, Topology Optimization in Structural Engineering, Numerical Analysis (math.NA), Mathematical Physics (math-ph), Computational Contact Mechanics and Variational Inequalities, FOS: Philosophy, ethics and religion, FOS: Psychology, Stiffness Optimization, Computational Theory and Mathematics, Mathematics - Classical Analysis and ODEs, Physical Sciences, Calibration, Convergence (economics), Medicine, FINITE ELEMENT, Finite element method, Dynamic relaxation, FOS: Physical sciences, Geometry, Structural engineering, QUASIVARIATIONAL INEQUALITY, Epistemology, Spring (device), Mathematical analysis, Quantum mechanics, UNILATERAL CONSTRAINT, FOS: Mathematics, Mathematics - Numerical Analysis, https://purl.org/becyt/ford/1, Economic growth, Civil and Structural Engineering, Non-linear Elastic Structures, Scheme (mathematics), Applied mathematics, Philosophy, Nonlinear Dynamics, Control and Systems Engineering, Dynamic Modeling, Computer Science, Nonlinear system, Simple (philosophy), Psychotherapist, Mathematics
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