Variational approach to relaxed topological optimization: closed form solutions for structural problems in a sequential pseudo-time framework

by   J. Oliver, et al.

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 characteristic function field as a topological design variable, (c) the consistent derivation of a relaxed topological derivative whose determination is simple, general and efficient, (d) formulation of the overall increasing cost function topological sensitivity as a suitable optimality criterion, and (e) consideration of a pseudo-time framework for the problem solution, ruled by the problem constraint evolution. In this setting, it is shown that the optimization problem can be analytically solved in a variational framework, leading to, nonlinear, closed-form algebraic solutions for the characteristic function, which are then solved, in every time-step, via fixed point methods based on a pseudo-energy cutting algorithm combined with the exact fulfillment of the constraint, at every iteration of the non-linear algorithm, via a bisection method. The issue of the ill-posedness (mesh dependency) of the topological solution, is then easily solved via a Laplacian smoothing of that pseudo-energy. In the aforementioned context, a number of (3D) topological structural optimization benchmarks are solved, and the solutions obtained with the explored closed-form solution method, are analyzed, and compared, with their solution through an alternative level set method. Although the obtained results, in terms of the cost function and topology designs, are very similar in both methods, the associated computational cost is about five times smaller in the closedform solution method this possibly being one of its advantages.


page 30

page 31

page 32

page 33

page 34

page 36

page 40


Topology optimization of thermal problems in a nonsmooth variational setting: closed-form optimality criteria

This paper extends the nonsmooth Relaxed Variational Approach (RVA) to t...

Topology optimization under thermo-elastic buckling

The focus of this paper is on topology optimization of continuum structu...

Non-linear Topology Optimization of District Heating Networks: A benchmark of Mixed-Integer and Adjoint Approaches

The widespread use of optimization methods in the design phase of Distri...

Solving Recurrence Relations using Machine Learning, with Application to Cost Analysis

Automatic static cost analysis infers information about the resources us...

Interference Exploitation Precoding Made Practical: Closed-Form Solutions with Optimal Performance

In this paper, we propose closed-form precoding schemes with optimal per...

Towards a multigrid method for the M1 model for radiative transfer

We present a geometric multigrid solver for the M1 model of radiative tr...

Variational Path Optimization of Linear Pentapods with a Simple Singularity Variety

The class of linear pentapods with a simple singularity variety is obtai...

Please sign up or login with your details

Forgot password? Click here to reset