Постановка задачі топологічної оптимізації конструкцій автомобілів та сільськогосподарської техніки

Problem. The demand for lightweight, durable, and efficient automobile and agricultural machinery structures requires advanced design methods. Topology optimization offers a solution by optimizing material distribution, but its application to complex structures is challenging due to varying loads and constraints. This study focuses on formulating the topology optimization problem to enhance structural efficiency and performance. Purpose. The primary goal of this paper is to contribute to the advancement of the scientific foundation of topology structural optimization, with a particular focus on tackling the complex optimization challenges encountered in automobile and agricultural machinery design. Methodology. Mathematical programming and modeling play a crucial role as foundational tools in the formulation of topology structural optimization problems within the automobile and agricultural machinery industry. Together, these tools facilitate the development of optimized structural designs that are not only lightweight and cost-effective but also capable of withstanding the demanding operational environments of agricultural equipment and automobiles. Results. This paper provides a short review and analysis of the current state of topology structural optimization. It presents both the classical variational formulation and the finite element formulation of the topology optimization problem. The study specifically addresses the problem of minimizing structural mass under stress constraints. The specific highlights are made for formulating the problem of topology optimization of agricultural machinery mechanical structures. The theory is applicable both for agricultural machinery and automobiles. Originality. This work focuses on the advancement of optimal design theory specifically tailored to address unique challenges in the design of automobile and agricultural machinery structures. To meet these needs, the study develops optimization approaches that integrate the specific mechanical, functional, and economic requirements of automobiles and agricultural equipment. Practical meaning. The practical value of this research lies in its adaptation of existing topology structural optimization problem formulations to address the specific challenges and requirements of the automobile and agricultural machinery industry. This adaptation ensures that the optimization solutions are not only mathematically sound but also practically viable, enabling the design of robust, efficient, and cost-effective heavy machinery components.