Topological Sensitivity Analysis for the Anisotropic Laplace Problem

This paper is concerned with the reconstruction of objects immersed in anisotropic media from boundary measurements. The aim of this paper is to propose an alternative approach based on the Kohn-Vogelius formulation and the topological sensitivity analysis method. The idea is to formulate the reconstruction problem as a topology optimization one minimizing an energy-like function. We derive a topological asymptotic expansion for the anisotropic Laplace operator. The unknown object is reconstructed using level-set curve of the topological gradient. We make finally some numerical examples proving the efficiency and accuracy of the proposed algorithm.

Topological sensitivity analysis with respect to a small idealized bolt

PurposeThis paper is devoted to the theoretical and numerical study of a new topological sensitivity concerning the insertion of a small bolt connecting two parts in a mechanical structure. First, an idealized model of bolt is proposed which relies on a non-local interaction between the two ends of the bolt (head and threads) and possibly featuring a pre-stressed state. Second, a formula for the topological sensitivity of such an idealized bolt is rigorously derived for a large class of objective functions. Third, numerical tests are performed in 2D and 3D to assess the efficiency of the bolt topological sensitivity in the case of no pre-stress. In particular, the placement of bolts (acting then as springs) is coupled to the further optimization of their location and to the shape and topology of the structure for volume minimization under compliance constraint.Design/methodology/approachThe methodology relies on the adjoint method and the variational formulation of the linearized elasticity equations in order to establish the topological sensitivity.FindingsThe numerical results prove the influence of the number and locations of the bolts which strongly influence the final optimized design of the structure.Originality/valueThis paper is the first one to study the topology optimization of bolted systems without a fixed prescribed number of bolts.

Topology Optimization Considering Porosity Defects in Metal Additive Manufacturing

In this paper, considering the porosity defects of Additive Manufacturing (AM), a level set topology optimization method for AM with porosity constraints is proposed. The concept of topological sensitivity is used to formulate a global porosity constraint function in the proposed method, and a level set topology optimization model considering porosity defects is obtained. To improve the robustness of the algorithm, the topology optimization model is solved in two phases. At first, the classical level set method without the porosity constraint is used to initially optimize the structure. During this process, the hole nucleation method combining bi-directional evolutionary structural optimization (BESO) and the topological sensitivity is used. Secondly, the topology optimization considering the effects of porosity is implemented on the preliminary optimization results. After performing the two-step optimization, a robust structure that alleviates the harmful impact of porosity defects is obtained. Finally, the robustness and effectiveness of the proposed method are validated by several two-dimensional numerical examples.

Application of the topological sensitivity method to the reconstruction of plasma equilibrium domain in a tokamak

The topological sensitivity method is an optimization technique used in different inverse problem solutions. In this work, we adapt this method to the identification of plasma domain in a Tokamak. An asymptotic expansion of a considered shape function is established and used to solve this inverse problem. Finally, a numerical algorithm is developed and tested in different configurations.

A Hole Nucleation Method Combining BESO and Topological Sensitivity for Level Set Topology Optimization

As is known to all, the incapacity to nucleate holes automatically in the design domain is one of the main issues of the classical level set topology optimization method. To solve the issue of hole nucleation, this paper employs the bi-directional evolutionary structural optimization (BESO) method based on the material removal scheme and the frequently used topological sensitivity and proposes the combining BESO and topological sensitivity (CBT) method for level set topology optimization. This method can replace the existing hole nucleation method for level set topology optimization. First, the topological sensitivity is combined with BESO, and the BESO method based on topological sensitivity is proposed. Second, the method is integrated into level set topology optimization to solve the issue of hole nucleation. Two sensitivity thresholds are defined depending on the evolutionary volume ratio and boundary topological sensitivity, respectively, and the smaller one is used as the sensitivity threshold for hole nucleation. The material is removed from the design domain to nucleate holes based on this threshold. Three classical two-dimensional numerical examples are used to validate the proposed hole nucleation method.

Non-Invasive Testing of Physical Systems Using Topological Sensitivity

A review of available results on non-destructive testing of physical systems, using the concept of topological sensitivity, is presented. This mathematical tool estimates the sensitivity of a set of measurements in some given sensors, distributed along the system, to defects/flaws that produce a degradation of the system. Such degradation manifests itself on the properties of the system. The good performance of this general purpose post-processing method is reviewed and illustrated in some applications involving non-destructive testing. These applications include structural health monitoring, considering both elastodynamic ultrasonic guided Lamb waves and active infrared thermography. Related methods can also be used in other fields, such as diagnosis/prognosis of engineering devices, which is also considered.

Topological sensitivity analysis for a three-dimensional parabolic type problem

This work focuses on the topological sensitivity analysis of a three-dimensional parabolic type problem. The considered application model is described by the heat equation. We derive a new topological asymptotic expansion valid for various shape functions and geometric perturbations of arbitrary form. The used approach is based on a rigorous mathematical framework describing and analyzing the asymptotic behavior of the perturbed temperature field.