Abstract
In this paper, we propose to use a modified SIMP method to solve the problem of topological optimization of structures from multiphase materials, i.e., structures containing components from more than two different materials, which must be distributed in the best way to obtain the best structural characteristics using only one design variable. Most problems of topological optimization are concerned with only one material and void, although in some cases, it is of interest to have a look at the topology of structure with several phases of materials that is at the problems of topological optimization of the structure from multiphase materials. Nevertheless, most of presently known approaches to solve the problems of topological optimization of structures based on the multiphase materials involve introduction of additional design variables, thereby increasing computational costs. The paper, when solving the problem of topological optimization of structures from multiphase materials, uses a modified SIMP method to approximate the properties of materials. In this approach a material density is considered as an independent calculated variable and selected from a continuous range, then separated by discrete values of densities of each material phase. Other properties are considered as continuous functions of density. The proposed method does not involve introduction of additional variables for materials approximation and ensures a stable transition from one phase of material to another and non-dependence of estimated costs on the amount of materials under consideration. To demonstrate the simplicity and efficiency of the proposed solution, the paper gives the examples of solving topological optimization problems for various designs from multiphase materials. Due to its conceptual simplicity, the proposed method can be easily applied to any existing topological optimization problems. The examples described in the paper show that using this solution allows us to obtain reliable structures with improved mechanical characteristics, which can be used to solve real problems in designing and manufacturing of complex structures.
Highlights
В данной работе предлагается использование модифицированного метода SIMP для решения задачи топологической оптимизации конструкций, содержащих компоненты из более, чем двух различных материалов, которые необходимо распределить наилучшим образом так, чтобы получить наилучшие структурные характеристики конструкции с использованием одной непрерывной переменной проектирования
We propose to use a modified SIMP method to solve the problem of topological optimization of structures from multiphase materials, i.e., structures containing components from more than two different materials, which must be distributed in the best way to obtain the best structural characteristics using only one design variable
The paper, when solving the problem of topological optimization of structures from multiphase materials, uses a modified SIMP method to approximate the properties of materials
Summary
На рис. 1 приведен общий вид конструкции и граничные условия для задачи многокомпонентной топологической оптимизации. 1 приведен общий вид конструкции и граничные условия для задачи многокомпонентной топологической оптимизации. Конструкция содержит область оптимизации, которая включает в себя два и более материала, также конструкция может содержать технологические отверстия и включения. К границам приложены нагрузки интенсивности или применены условия жесткого закрепления, также граница может быть свободна от нагрузок, в зависимости от рассматриваемой задачи. 1. Схематическое изображение конструкции и граничных условий для многокомпонентной топологической оптимизации. В предлагаемом способе материалы сортируются по возрастанию нормированной плотности материала iT : i iT max (i 1, 2,3,..., m) ,. Где max — максимальная плотность из всех оптимизируемых материалов; iT — исходные плотности материалов; m — количество оптимизируемых материалов. Используя представление плотности (4), классическую степенную интерполяция (1) материала для случая многокомпонентной оптимизации можно записать в виде. Вид частного случая функции (5) для трех материалов приведен на рис. 2. Упорядоченная многокомпонентная SIMP-интерполяция модуля упругости дл трех материалов
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