Verification of shape optimization in nonstationary multi-physics problems

2022 Fiscal Year Final Research Report

• Project/Area Number: 18K03996
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Review Section: Basic Section 19020:Thermal engineering-related
• Research Institution: Gifu National College of Technology
• Principal Investigator: KATAMINE Eiji 岐阜工業高等専門学校, その他部局等, 教授 (00224452)
• Project Period (FY): 2018-04-01 – 2023-03-31
• Keywords: 最適設計 / 形状最適化 / 形状同定 / 連成問題 / 有限要素法 / 随伴変数法

Outline of Final Research Achievements

A numerical analysis method is proposed for shape determination problems in fundamental unsteady thermoelastic field and unsteady thermal convection field. In the thermoelastic field problem, the stiffness maximization problem, which determines the shape that minimizes the thermal deformation in the specified time period, was investigated. In the thermal convection field problem, a shape determination problem was set to control the temperature time history at the sub-boundary. For these shape design problems, the shape gradient function, which is the sensitivity of shape updating, was theoretically derived using the adjoint variable method. Numerical programs were developed to analyze the optimal shape based on the derived shape gradient function using FreeFEM. Based on the numerical results of the two-dimensional problem, the validity of the proposed solution was demonstrated.

Free Research Field

工学

Academic Significance and Societal Importance of the Research Achievements

時間発展型マルチフィジックス問題の形状最適化は，実際の設計現場において要求度の高い課題であるにも関わらず，理論に基づいた研究はこれまでほとんど実施されていなかった．そこで，基礎的な非定常熱弾性場と非定常熱対流場における形状決定問題に対して，最適設計理論等に基づいた数値解析法を提案して，その解析手法の妥当性を示すことができた．