Related papers: Shape and Topology Optimization involving the eige…
A local and parallel algorithm based on the multilevel discretization is proposed in this paper to solve the eigenvalue problem by the finite element method. With this new scheme, solving the eigenvalue problem in the finest grid is…
This paper presents a topology optimization approach for surface flows, which can represent the viscous and incompressible fluidic motions at the solid/liquid and liquid/vapor interfaces. The fluidic motions on such material interfaces can…
An optimization method for the design of multi-lattice structures satisfying local buckling constraints is proposed in this paper. First, the concept of free material optimization is introduced to find an optimal elastic tensor distribution…
The present work proposes an extension of the third medium contact method for solving structural topology optimization problems that involve and exploit self-contact. A new regularization of the void region, which acts as the contact…
Elastic valley metamaterials offer an excellent platform to manipulate elastic waves and have potential applications in energy harvesting and elastography. Here we introduce a series of strategies to realize topological transition in spiral…
This manuscript presents an approach for simultaneously optimizing the connectivity and elevation of grid-shell structures acting in pure compression (or pure tension) under the combined effects of a prescribed external loading and the…
It is well known that the solution of topology optimization problems may be affected both by the geometric properties of the computational mesh, which can steer the minimization process towards local (and non-physical) minima, and by the…
We investigate the problem of finding the optimal shape and topology of a system of acoustic lenses in a dissipative medium. The sound propagation is governed by a general semilinear strongly damped wave equation. We introduce a phase-field…
It is classical that, when the small deformation is assumed, the incremental analysis problem of an elastoplastic structure with a piecewise-linear yield condition and a linear strain hardening model can be formulated as a convex quadratic…
Optimization of frame structures is formulated as a~non-convex optimization problem, which is currently solved to local optimality. In this contribution, we investigate four optimization approaches: (i) general non-linear optimization, (ii)…
Topology optimization is used for the design of high-performance structures but remains fundamentally limited by its iterative nature, requiring repeated finite element analyses that prevent real-time deployment and large-scale design…
We study time- and parameter-dependent ordinary differential equations in the geometric setting of vector fields and their flows. Various degrees of regularities in state are considered, including Lipschitz, finitely diferentiable, smooth,…
With the development of multi-layer elastic systems in the field of engineering mechanics, the corresponding variational inequality theory and algorithm design have received more attention and research. In this study, a class of equivalent…
We establish an Alhfors-regularity result for minimizers of a multiphase optimal design problem. It is a variant of the classical variational problem which involves a finite number of chambers $\mathcal{E}(i)$ of prescribed volume that…
Many problems that arise in machine learning domain deal with nonlinearity and quite often demand users to obtain global optimal solutions rather than local optimal ones. Optimization problems are inherent in machine learning algorithms and…
The modeling of cracks has been an intensely researched topic for decades - both from the mechanical as well as from the mathematics point of view. As far as the modeling of sharp cracks/interfaces is concerned, the resulting free boundary…
This paper proposes topology optimization for considering shielding and penetrating features. Based on the fictitious physical model, which is a useful approach to control geometric features, the proposed method analyzes fictitious…
Particle flow processing is widely employed across various industrial applications and technologies. Due to the complex interactions between particles and fluids, designing effective devices for particle flow processing is challenging. In…
We describe the implementation of a topological constraint in finite element simulations of phase field models which ensures path-connectedness of preimages of intervals in the phase field variable. Two main applications of our method are…
We develop a new optimisation technique that combines multiresolution subdivision surfaces for boundary description with immersed finite elements for the discretisation of the primal and adjoint problems of optimisation. Similar to wavelets…