Book review: "Numerical Solutions of Partial Differential Equations" by S. Bertoluzza, S. Falletta, G. Ruso and Chi-Wang Shu
Topology optimization of systems governed by variational inequalities
This paper deals with the formulation of the necessary optimality condition for a topology optimization problem of an elastic body in unilateral contact with a rigid foundation. In the contact problem of Tresca, a given friction is governed by an elliptic variational inequality of the second order. The optimization problem consists in finding such topology of the domain occupied by the body that the normal contact stress along the contact boundary of the body is minimized. The topological derivative...
Shape optimization for dynamic contact problems
The paper deals with shape optimization of dynamic contact problem with Coulomb friction for viscoelastic bodies. The mass nonpenetrability condition is formulated in velocities. The friction coefficient is assumed to be bounded. Using material derivative method as well as the results concerning the regularity of solution to dynamic variational inequality the directional derivative of the cost functional is calculated and the necessary optimality condition is formulated.
Radial basis function level set method for structural optimization
Book review: "Global Pseudo-Differential Calculus on Euclidean Spaces" by F. Nicola and L. Rodino
Topology optimization of quasistatic contact problems
This paper deals with the formulation of a necessary optimality condition for a topology optimization problem for an elastic contact problem with Tresca friction. In the paper a quasistatic contact model is considered, rather than a stationary one used in the literature. The functional approximating the normal contact stress is chosen as the shape functional. The aim of the topology optimization problem considered is to find the optimal material distribution inside a design domain occupied by the...
Book review: "Linear Partial Differential Equations for Scientists and Engineers" by Tyn Myint-U, Lokenath Debnath
Book review: "Variational Methods in Shape Optimization Problems"
Book review: "Statistics and Analysis of Shape" by H. Krim, A. Yezzi, Jr., eds.
Book review: "A Handbook of Real Variables" by S.G. Krantz
Shape optimization of a nonlinear elliptic system
Hybrid level set phase field method for topology optimization of contact problems
The paper deals with the analysis and the numerical solution of the topology optimization of system governed by variational inequalities using the combined level set and phase field rather than the standard level set approach. The standard level set method allows to evolve a given sharp interface but is not able to generate holes unless the topological derivative is used. The phase field method indicates the position of the interface in a blurry way but is flexible in the holes generation. In the...
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