Seung Hyun Jeong

Toward a stress-based topology optimization procedure with indirect calculation of internal finite element information

Abstract In this work, a novel computational approach is developed for the gradient-based stress-based topology optimization method, where the volume is minimized according to locally defined stress constraints of static failure criteria in the framework of tailored finite element (FE) software without direct access to an internal finite element information database. Tailored finite element codes that require substantial understanding and modification (reprogramming) or do not directly provide internal finite element information have rarely been used for stress-based topology optimization with solid isotropic material with penalization (SIMP) methods. Therefore, much research has been confined to two-dimensional problems with rectilinear basic finite elements, as complex three-dimensional geometries with advanced finite element formulations are not supported. To overcome this problem, we developed a new computational procedure for sensitivity analysis without direct access to an internal information database, a task that has previously been regarded as almost impossible. Since the calculation of linear strain–displacement matrices is required in the sensitivity analysis, the present procedure includes a node selection algorithm to efficiently calculate the matrices of irregular-shaped finite elements by displacement perturbations. The benefits of the present approach are that well-established powerful finite element codes, i.e., commercial or sophisticated public FE codes, can be easily incorporated for linear stress-based topology optimization, and any type of finite element formulation can be readily employed. In contrast to classical sensitivity analysis, small computations are used for sensitivity analysis in this work. To demonstrate the validity and efficiency of the present procedure and approach, several topology optimization problems with 3D and shell elements are solved.

Topology optimization considering fatigue life in the frequency domain

This research develops a new topological optimization (TO) method to assess dynamic fatigue failure in the frequency domain for random excitation forces. Besides static failure, fatigue life (or fatigue failure) is an important design criterion for the safety of mechanical and building structures. Therefore, many assessment theories and computational approaches have been proposed, and they can be divided into two categories: time domain and frequency domain. Although both approaches have been successfully applied for engineering purposes, they are rarely considered in structural TO. To consider fatigue failure caused by stochastic mechanical loads in structural TO, this research adopts fatigue assessment approaches in the frequency domain, such as narrow band solution, the Wirsching and Light method, the Ortiz and Chen method, and Dirlik method. For TO, we perform an adjoint sensitivity analysis with those fatigue assessment methods. We consider some two-dimensional benchmark problems and show that the present design method successfully constrains fatigue.

Motion Structural Optimization Strategy for Rhombic Element Based Foldable Structure

This research presents a new systematical design approach of foldable structure composed of several rhombic elements by applying genetic algorithm. As structural shapes represented by a foldable structure can be easily and dramatically morphed by manipulating rotational directions and angle of joints, the foldable structure has been used for various elementary structural members and engineering mechanisms. However a systematic design approach determining detail rotational angle and directions of unit cells for arbitrary shaped target areas has not been proposed yet. This research contributes to it by developing a new structural optimization method determining optimal angle and rotation directions to cover arbitrary shaped target areas of interest with aggregated rhombic elements. To achieve this purpose, we present an optimization formulation minimizing the sum of distances between each reference joint of an arbitrary shaped target area and its closest outer joints of foldable structure. To find out the outer joint set of a given foldable structure, an efficient geometric analysis method based on Delaunay triangulation is also developed and implemented. To show the validity and limitations of the present approach, several foldable structure design problems for two-dimensional arbitrary shaped target areas are solved with the present optimization procedure.