Related papers: Revisiting topology optimization with buckling con…
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…
This paper proposes a topology optimization method that considers the geometric constraint of no closed cavities to improve the effectiveness of additive manufacturing based on the fictitious physical model approach. First, the basic…
In this paper, we consider an imperfect finite beam lying on a nonlinear foundation, whose dimensionless stiffness is reduced from $1$ to $k$ as the beam deflection increases. Periodic equilibrium solutions are found analytically and are in…
To reduce the stress concentration and ensure the structural safety for lattice structure designs, in this paper, a new optimization framework is developed for the optimal design of graded lattice structures, innovatively integrating fillet…
In this article a topology optimization method is developed, which is aware of material uncertainties. The uncertainties are handled in a worst-case sense, i.e. the worst possible material distribution over a given uncertainty set is taken…
We look for minimizers of the buckling load problem with perimeter constraint in any dimension. In dimension 2, we show that the minimizing plates are convex; in higher dimension, by passing through a weaker formulation of the problem, we…
We give a unified treatment to optimization problems that can be expressed in the form of nonnegative-real-weighted Boolean constraint satisfaction problems. Creignou, Khanna, Sudan, Trevisan, and Williamson studied the complexity of…
The work explores a specific scenario for structural computational optimization based on the following elements: (a) a relaxed optimization setting considering the ersatz (bi-material) approximation, (b) a treatment based on a nonsmoothed…
This contribution examines optimization problems that involve stochastic dominance constraints. These problems have uncountably many constraints. We develop methods to solve the optimization problem by reducing the constraints to a finite…
This paper presents a density-based topology optimization approach to design structures under self-weight load. Such loads change their magnitude and/or location as the topology optimization advances and pose several unique challenges,…
This work proposes a novel theoretical framework of robust limit analysis i.e. the computation of limit loads of structures in presence of uncertainties using limit analysis and robust optimization theories. We first derive generic robust…
The standard approach to supervised classification involves the minimization of a log-loss as an upper bound to the classification error. While this is a tight bound early on in the optimization, it overemphasizes the influence of…
In this work we consider topology optimization of systems, which are governed by the external Bernoulli free boundary problem. We utilize the so-called pseudo-solid approach to solve the governing free boundary problems during the…
Interest in components with detailed structures increased with the progress in advanced manufacturing techniques in recent years. Parts with graded lattice elements can provide interesting mechanical, thermal, and acoustic properties…
Structural stiffness plays an important role in engineering design. The analysis of stiffness requires precise experiments and computational models that can be difficult or time-consuming to procure. A novel relation between modal and…
The robust topology optimization formulation that introduces the eroded and dilated versions of the design has gained increasing popularity in recent years, mainly because of its ability to produce designs satisfying a minimum length scale.…
This paper studies the problem of maximizing a monotone submodular function under an unknown knapsack constraint. A solution to this problem is a policy that decides which item to pack next based on the past packing history. The robustness…
We analyze the convergence rate of various momentum-based optimization algorithms from a dynamical systems point of view. Our analysis exploits fundamental topological properties, such as the continuous dependence of iterates on their…
We study a new penalty reformulation of constrained convex optimization based on the softplus penalty function. We develop novel and tight upper bounds on the objective value gap and the violation of constraints for the solutions to the…
Purpose: This is an attempt to better bridge the gap between the mathematical and the engineering/physical aspects of the topic. We trace the different sources of non-convexification in the context of topology optimization problems starting…