scholarly journals Continuous dependence and optimal control of a dynamic elastic-viscoplastic contact problem with non-monotone boundary conditions

2022 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Xilu Wang ◽  
Xiaoliang Cheng
Keyword(s):  
Optimal Control ◽  
Boundary Conditions ◽  
Continuous Dependence ◽  
Initial Conditions ◽  
Weak Form ◽  
Constitutive Law ◽  
Optimal Solutions ◽  
Existence Of Optimal Solutions ◽  
External Forces ◽  
Weak Topologies

<p style='text-indent:20px;'>In this paper, we consider continuous dependence and optimal control of a dynamic elastic-viscoplastic contact model with Clarke subdifferential boundary conditions. Since the constitutive law of elastic-viscoplastic materials has an implicit expression of the stress field, the weak form of the model is an evolutionary hemivariational inequality coupled with an integral equation. By providing some equivalent weak formulations, we prove the continuous dependence of the solution on external forces and initial conditions in the weak topologies. Finally, the existence of optimal solutions to a boundary optimal control problem is established.</p>

Meshless Integral Method for Analysis of Elastoplastic Geotechnical Materials

2010 ◽  
Author(s):  
Jianfeng Ma ◽  
Joshua David Summers ◽  
Paul F. Joseph
Keyword(s):  
Boundary Conditions ◽  
Function Approximation ◽  
Integral Method ◽  
Weak Form ◽  
Constitutive Law ◽  
Governing Equations ◽  
Natural Boundary ◽  
Pressure Sensitive ◽  
Support Domain ◽  
Natural Boundary Conditions

The meshless integral method based on regularized boundary equation [1][2] is extended to analyze elastoplastic geotechnical materials. In this formulation, the problem domain is clouded with a node set using automatic node generation. The sub-domain and the support domain related to each node are also generated automatically using algorithms developed for this purpose. The governing integral equation is obtained from the weak form of elastoplasticity over a local sub-domain and the moving least-squares approximation is employed for meshless function approximation. The geotechnical materials are described by pressure-sensitive multi-surface Drucker-Prager/Cap plasticity constitutive law with hardening. A generalized collocation method is used to impose the essential boundary conditions and natural boundary conditions are incorporated in the system governing equations. A comparison of the meshless results with the FEM results shows that the meshless integral method is accurate and robust enough to solve geotechnical materials.

scholarly journals Optimal control of nonlinear second order evolution equations

1993 ◽  
Vol 6 (2) ◽  
pp. 123-135 ◽  
Author(s):  
N. U. Ahmed ◽  
Sebti Kerbal
Keyword(s):  
Optimal Control ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Second Order ◽  
Nonlinear Evolution Equations ◽  
Optimal Solutions ◽  
Existence Of Optimal Solutions ◽  
Lagrange Problem

In this paper we study the optimal control of systems governed by second order nonlinear evolution equations. We establish the existence of optimal solutions for Lagrange problem.

Optimal control of static contact in finite strain elasticity

2020 ◽  
Vol 26 ◽  
pp. 95
Author(s):  
Anton Schiela ◽  
Matthias Stoecklein
Keyword(s):  
Optimal Control ◽  
Finite Strain ◽  
Path Following ◽  
Contact Problems ◽  
Finite Deformations ◽  
Elastic Contact ◽  
Optimal Solutions ◽  
Existence Of Optimal Solutions ◽  
Static Contact ◽  
Convergence Of Sequences

We consider the optimal control of elastic contact problems in the regime of finite deformations. We derive a result on existence of optimal solutions and propose a regularization of the contact constraints by a penalty formulation. Subsequential convergence of sequences of solutions of the regularized problem to original solutions is studied. Based on these results, a numerical path-following scheme is constructed and its performance is tested.

scholarly journals SOLUTION TO THE OPTIMAL CONTROL PROBLEM BY SOURCES IN THE BOUNDARY CONDITIONS OF A HYPERBOLIC SYSTEM OF A NETWORK STRUCTURE

2021 ◽  
Vol 8 (1) ◽  
pp. 004-012
Author(s):  
Y. R. Ashrafova ◽  
◽  
S. R. Rasulova ◽  
◽  
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Boundary Conditions ◽  
Control Problem ◽  
Initial Conditions ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Distributed Parameters ◽  
Long Duration ◽  
Internal Sources

The solution to the optimal control problem by power of external and internal sources acting on the multilink system in nonlocal boundary conditions is investigated. Each arc of the system is an object with distributed parameters, described by a differential equation of hyperbolic type and related only by boundary values, and in an arbitrary way. Due to the long duration of the object's functioning, the exact values of the initial conditions are not known, but a set of their possible values is given. Based on the results of additional measurements of the state of the process at the input or output ends of the arcs (which are not internal vertices), a target functional is constructed, for which minimization a formula for its gradient is obtained.

scholarly journals Optimal Control of a Nonlinear PDE Governed by Fractional Laplacian

2021 ◽  
Author(s):  
Rafał Kamocki
Keyword(s):  
Optimal Control ◽  
Fractional Laplacian ◽  
Nonlinear Pde ◽  
Optimal Solutions ◽  
Dirichlet Laplacian ◽  
Existence Of Optimal Solutions ◽  
Closure Theorem ◽  
Orientor Fields ◽  
Lower Closure ◽  
Lower Closure Theorem

AbstractWe consider an optimal control problem containing a control system described by a partial nonlinear differential equation with the fractional Dirichlet–Laplacian, associated to an integral cost. We investigate the existence of optimal solutions for such a problem. In our study we use Filippov’s approach combined with a lower closure theorem for orientor fields.

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