29,871 research outputs found
Energy consistent nonlinear dynamic contact analysis of structures
This work is motivated by the need for a numerically stable dynamic contact algorithm, for use with finite element (FE) analysis including both material and geometric nonlinearities, which imposes the appropriate full kinematic compatibility between the interfaces of impacting boundaries during a persistent dynamic contact.
Several methods were previously developed based on Lagrangian multipliers or penalty functions in an attempt to impose the impenetrability condition of dynamic contact analysis. Some of these existing algorithms suffer from lack of numerical stability, and most of them are incapable of accurately predicting the persistent contact force, hence they would not be suitable for frictional dynamic contact analysis.
The numerical stability and energy conservation characteristics of conventional frictionless dynamic contact algorithms using Lagrangian displacement constraints and penalty functions are investigated in this thesis. Two energy controlling dynamic contact algorithms are proposed in conjunction with the well-known Newmark trapezoidal rule, namely, regularised penalty method and Lagrangian velocity constraint. Although energy consistent, the state of the art for these two methods is somewhat similar to the conventional displacement constraints in the sense that acceleration compatibility is not imposed when simulating problems featuring persistent dynamic contact.
In this work, a novel and superior energy controlling-algorithm is proposed which overcomes the aforementioned shortcomings. The proposed DVA method enforces the displacement, velocity and acceleration compatibilities (referred to as DVA constraint in this work) between the impacting interfaces, which in contrast to existing algorithms can be used for FE analysis of problems exhibiting geometric and material nonlinearities. The advanced DVA method is devised such that the kinematic compatibilities at the interface are consistent with the solution for a continuous system without any special treatment in the time-integration or solution procedure of the penetrating interface boundaries. Furthermore, this can be achieved in conjunction with all of the prevalent implicit time-integration schemes such as the trapezoidal rule, midpoint rule, HHT-α and the most recently developed Energy-Momentum family of Methods.
Finally, utilising the proposed dynamic contact algorithms, a novel multi-constraints node-to-surface dynamic contact element is formulated and programmed within a geometric and material nonlinear dynamic FE analysis software. Several verification examples of frictionless mechanical contact are presented to demonstrate the superiority and performance of the developed node-to-surface contact element in conjunction with the proposed DVA constraint as well as the Lagrangian velocity constraint, providing a robust and accurate solution procedure for highly nonlinear dynamic contact analysis.Open Acces
A Primal-Dual Augmented Lagrangian
Nonlinearly constrained optimization problems can be solved by minimizing a sequence of simpler unconstrained or linearly constrained subproblems. In this paper, we discuss the formulation of subproblems in which the objective is a primal-dual generalization of the Hestenes-Powell augmented Lagrangian function. This generalization has the crucial feature that it is minimized with respect to both the primal and the dual variables simultaneously. A benefit of this approach is that the quality of the dual variables is monitored explicitly during the solution of the subproblem. Moreover, each subproblem may be regularized by imposing explicit bounds on the dual variables. Two primal-dual variants of conventional primal methods are proposed: a primal-dual bound constrained Lagrangian (pdBCL) method and a primal-dual 1 linearly constrained Lagrangian (pd1-LCL) method
Mechanical Systems with Symmetry, Variational Principles, and Integration Algorithms
This paper studies variational principles for mechanical systems with symmetry and their applications to integration algorithms. We recall some general features of how to reduce variational principles in the presence of a symmetry group along with general features of integration algorithms for mechanical systems. Then we describe some integration algorithms based directly on variational principles using a
discretization technique of Veselov. The general idea for these variational integrators is to directly discretize Hamilton’s principle rather than the equations of motion in a way that preserves the original systems invariants, notably the symplectic form and, via a discrete version of Noether’s theorem, the momentum map. The resulting mechanical integrators are second-order accurate, implicit, symplectic-momentum algorithms. We apply these integrators to the rigid body and the double spherical pendulum to show that the techniques are competitive with existing integrators
Design optimization applied in structural dynamics
This paper introduces the design optimization strategies, especially for structures which have dynamic constraints. Design optimization involves first the modeling and then the optimization of the problem. Utilizing the Finite Element (FE) model of a structure directly in an optimization process requires a long computation time. Therefore the Backpropagation Neural Networks (NNs) are introduced as a so called surrogate model for the FE model. Optimization techniques mentioned in this study cover the Genetic Algorithm (GA) and the Sequential Quadratic Programming (SQP) methods. For the applications of the introduced techniques, a multisegment cantilever beam problem under the constraints of its first and second natural frequency has been selected and solved using four different approaches
A sequential semidefinite programming method and an application in passive reduced-order modeling
We consider the solution of nonlinear programs with nonlinear
semidefiniteness constraints. The need for an efficient exploitation of the
cone of positive semidefinite matrices makes the solution of such nonlinear
semidefinite programs more complicated than the solution of standard nonlinear
programs. In particular, a suitable symmetrization procedure needs to be chosen
for the linearization of the complementarity condition. The choice of the
symmetrization procedure can be shifted in a very natural way to certain linear
semidefinite subproblems, and can thus be reduced to a well-studied problem.
The resulting sequential semidefinite programming (SSP) method is a
generalization of the well-known SQP method for standard nonlinear programs. We
present a sensitivity result for nonlinear semidefinite programs, and then
based on this result, we give a self-contained proof of local quadratic
convergence of the SSP method. We also describe a class of nonlinear
semidefinite programs that arise in passive reduced-order modeling, and we
report results of some numerical experiments with the SSP method applied to
problems in that class
Aggregate constrained inventory systems with independent multi-product demand: control practices and theoretical limitations
In practice, inventory managers are often confronted with a need to consider one or more aggregate constraints. These aggregate constraints result from available workspace, workforce, maximum investment or target service level. We consider independent multi-item inventory problems with aggregate constraints and one of the following characteristics: deterministic leadtime demand, newsvendor, basestock policy, rQ policy and sS policy. We analyze some recent relevant references and investigate the considered versions of the problem, the proposed model formulations and the algorithmic approaches. Finally we highlight the limitations from a practical viewpoint for these models and point out some possible direction for future improvements
Multiplier-continuation algorthms for constrained optimization
Several path following algorithms based on the combination of three smooth penalty functions, the quadratic penalty for equality constraints and the quadratic loss and log barrier for inequality constraints, their modern counterparts, augmented Lagrangian or multiplier methods, sequential quadratic programming, and predictor-corrector continuation are described. In the first phase of this methodology, one minimizes the unconstrained or linearly constrained penalty function or augmented Lagrangian. A homotopy path generated from the functions is then followed to optimality using efficient predictor-corrector continuation methods. The continuation steps are asymptotic to those taken by sequential quadratic programming which can be used in the final steps. Numerical test results show the method to be efficient, robust, and a competitive alternative to sequential quadratic programming
Projection methods in conic optimization
There exist efficient algorithms to project a point onto the intersection of
a convex cone and an affine subspace. Those conic projections are in turn the
work-horse of a range of algorithms in conic optimization, having a variety of
applications in science, finance and engineering. This chapter reviews some of
these algorithms, emphasizing the so-called regularization algorithms for
linear conic optimization, and applications in polynomial optimization. This is
a presentation of the material of several recent research articles; we aim here
at clarifying the ideas, presenting them in a general framework, and pointing
out important techniques
Optimization Methods for Inverse Problems
Optimization plays an important role in solving many inverse problems.
Indeed, the task of inversion often either involves or is fully cast as a
solution of an optimization problem. In this light, the mere non-linear,
non-convex, and large-scale nature of many of these inversions gives rise to
some very challenging optimization problems. The inverse problem community has
long been developing various techniques for solving such optimization tasks.
However, other, seemingly disjoint communities, such as that of machine
learning, have developed, almost in parallel, interesting alternative methods
which might have stayed under the radar of the inverse problem community. In
this survey, we aim to change that. In doing so, we first discuss current
state-of-the-art optimization methods widely used in inverse problems. We then
survey recent related advances in addressing similar challenges in problems
faced by the machine learning community, and discuss their potential advantages
for solving inverse problems. By highlighting the similarities among the
optimization challenges faced by the inverse problem and the machine learning
communities, we hope that this survey can serve as a bridge in bringing
together these two communities and encourage cross fertilization of ideas.Comment: 13 page
- …