Kh. Soleymanian, S. M. Tavakkoli,
Volume 15, Issue 2 (4-2025)
Abstract
This study aims to deal with multi-material topology optimization problems by using the Methods of Moving Asymptotes (MMA) method. The optimization problem is to minimize the strain energy while a certain amount of material is used. Several types of structures, including plane, plate and shell structures, are considered and optimal materials distribution is investigated. To parametrize the topology optimization problem, the Solid Isotropic Material with Penalization (SIMP) method is utilized. Analytical sensitivity analysis is performed to obtain the derivatives of the objective function and volume constraints with respect to the design variables. Two types of material with different modulus of elasticities are considered and, therefore, each element has two design variables. The first design variable represents the presence or absence of material in an element, while the second design variable determines the type of material assigned to the element. In order to analyze the structures required during the optimization process, the ABAQUS software is employed. To integrate the topology optimization procedure with ABAQUS model, a Python script is developed. The obtained results demonstrate the performance of the proposed method in generating reasonable and effective topologies.
P. Rajabi , S. M. Tavakkoli,
Volume 16, Issue 1 (1-2026)
Abstract
This paper presents a method for detecting the location and severity of damage in shell structures. The method relies on extracting time-domain damage-sensitive features from vibrational responses and applying topology optimization. To achieve this, singular values are extracted from the Hankel matrix using singular value (SVD) decomposition and selected as damage-sensitive features. The damage detection problem is formulated as a topology optimization problem in which damage is modeled using the solid isotropic material with penalization (SIMP) method. Sensitivity analysis is carried out using the finite difference method to compute the derivatives of the objective function with respect to the design variables, thereby enabling efficient gradient-based optimization. The objective function is defined to minimize the differences between the singular values of the reference structure and those of the model. Abaqus software is used to perform dynamic finite element analysis of the shell model and to derive acceleration responses at selected nodes, which serve as sensor locations. The results from several numerical examples demonstrate the high capability of the proposed method in accurately identifying both the location and severity of damage.
