Mihai Anitescu

Large-Scale Parallel Multibody Dynamics with Frictional Contact on the Graphical Processing Unit

  • Mihai Anitescu
  • Dan Negrut
  • Alessandro Tasora
    • Categories Complementarity and Variational Inequalities, Mechanical Engineering, Second-Order Cone Programming Tags , ,

    In the context of simulating the frictional contact dynamics of large systems of rigid bodies, this paper reviews a novel method for solving large cone complementarity problems by means of a fixed-point iteration algorithm. The method is an extension of the Gauss-Seidel and Gauss-Jacobimethods with overrelaxation for symmetric convex linear complementarity problems. Convergent under fairly … Read more

    An iterative approach for cone complementarity problems for nonsmooth multibody dynamics

  • Mihai Anitescu
  • Alessandro Tasora
    • Categories Complementarity and Variational Inequalities, Convex Optimization, Mechanical Engineering

    Aiming at a fast and robust simulation of large multibody systems with contacts and friction, this work presents a novel method for solving large cone complementarity problems by means of a fixed-point iteration. The method is an extension of the Gauss-Seidel and Gauss-Jacobi method with overrelaxation for symmetric convex linear complementarity problems. The method is … Read more

    SPECTRAL STOCHASTIC FINITE-ELEMENT METHODS FOR PARAMETRIC CONSTRAINED OPTIMIZATION PROBLEMS

  • Mihai Anitescu
    • Categories Constrained Nonlinear Optimization, Mechanical Engineering, Stochastic Programming Tags , , , ,

    We present a method to approximate the solution mapping of parametric constrained optimization problems. The approximation, which is of the spectral stochastic finite element type, is represented as a linear combination of orthogonal polynomials. Its coefficients are determined by solving an appropriate finite-dimensional constrained optimization problem. We show that, under certain conditions, the latter problem … Read more

    CONVERGENCE OF A CLASS OF SEMI-IMPLICIT TIME-STEPPING SCHEMES FOR NONSMOOTH RIGID MULTIBODY DYNAMICS

  • Mihai Anitescu
  • Florian A. Potra
  • Bogdan Gavrea
    • Categories Complementarity and Variational Inequalities, Mechanical Engineering, Other Topics Tags , , , ,

    In this work we present a framework for the convergence analysis in a measure differential inclusion sense of a class of time-stepping schemes for multibody dynamics with contacts, joints, and friction. This class of methods solves one linear complementarity problem per step and contains the semi-implicit Euler method, as well as trapezoidallike methods for which … Read more

    Elastic-Mode Algorithms for Mathematical Programs with Equilibrium Constraints: Global Convergence and Stationarity Properties

  • Mihai Anitescu
  • Paul Tseng
  • Stephen Wright
    • Categories Complementarity and Variational Inequalities, Constrained Nonlinear Optimization Tags , , , , , ,

    The elastic-mode formulation of the problem of minimizing a nonlinear function subject to equilibrium constraints has appealing local properties in that, for a finite value of the penalty parameter, local solutions satisfying first- and second-order necessary optimality conditions for the original problem are also first- and second-order points of the elastic-mode formulation. Here we study … Read more

    GLOBAL CONVERGENCE OF AN ELASTIC MODE APPROACH FOR A CLASS OF MATHEMATICAL PROGRAMS WITH COMPLEMENTARITY CONSTRAINTS

  • Mihai Anitescu
    • Categories Complementarity and Variational Inequalities, Constrained Nonlinear Optimization, Mechanical Engineering Tags , , ,

    We prove that any accumulation point of an elastic mode approach, applied to the optimization of a mixed P variational inequality, that approximately solves the relaxed subproblems is a C-stationary point of the problem of optimizing a parametric mixed P variational inequality. If, in addition, the accumulation point satis es the MPCC-LICQ constraint quali cation and if … Read more

    ON USING THE ELASTIC MODE IN NONLINEAR PROGRAMMING APPROACHES TO MATHEMATICALPROGRAMS WITH COMPLEMENTARITY CONSTRAINTS

  • Mihai Anitescu
    • Categories Complementarity and Variational Inequalities, Constrained Nonlinear Optimization Tags , , , , ,

    We investigate the possibility of solving mathematical programs with complementarity constraints (MPCCs) using algorithms and procedures of smooth nonlinear programming. Although MPCCs do not satisfy a constraint qualification, we establish sucient conditions for their Lagrange multiplier set to be nonempty. MPCCs that have nonempty Lagrange multiplier sets and that satisfy the quadratic growth condition can … Read more

    OPTIMIZATION-BASED SIMULATION OF NONSMOOTH RIGID MULTIBODY DYNAMICS

  • Mihai Anitescu
    • Categories Complementarity and Variational Inequalities, Mechanical Engineering Tags , , , ,

    We present a time-stepping method to simulate rigid multibody dynamics with inelastic collision, contact, and friction. The method progresses with fixed time step without backtracking for collision and solves at every step a strictly convex quadratic program. We prove that a solution sequence of the method converges to the solution of a measure differential inclusion. … Read more