This study develops a two-dimensional design sensitivity analysis and topology optimization method for multi-objective problems considering both thermal insulation and structural stiffness. The objective function is defined by introducing a weight factor that combines the thermal total energy and compliance for the thermal and structural problems. The derived design sensitivities are validated using the finite difference sensitivities. The Pareto front for designing thermal insulation is obtained by varying the weight function of the objective function and size of the domain. This meant that the geometric feature of the thermal bottleneck outweighed the load-supporting structures as the relative importance of the thermal insulation increased. Compared with the existing designs, the obtained designs are both structurally reliable and thermally insulative in terms of quantitative performance measures.

한국전산구조공학회 논문집 제37권 제5호(2024.10) 309 1. 서 론 복합소재 3D 프린팅 공정 기술은 부품 출력 과정에서 다양 한 소재 적용 및 높은 형상 자유도 구현이 가능하며, 이를 통해 구조용 부품 제작 과정에서 기존의 성형 공법들과는 차별화된 방식으로 고강도 경량 특성을 구현할 수 있다는 장점이 있다.

We present a design sensitivity analysis and isogeometric shape optimization with path-dependent loads belonging to non-conservative loads under the assumption of elastic bodies. Path-dependent loads are sometimes expressed as the follower forces, and these loads have characteristics that depend not only on the design area of the structure but also on the deformation. When such a deformation-dependent load is considered, an asymmetric load stiffness matrix (tangential operator) in the response region appears. In this paper, the load stiffness matrix is derived by linearizing the non-linear non-conservative load, and the geometrical non-linear structure is optimally designed in the total Lagrangian formulation using the isogeometric framework. In particular, since the deformation-dependent load changes according to the change and displacement of the design area, the isogeometric analysis has a significant influence on the accuracy of the sensitivity analysis and optimization results. Through several numerical examples, the applicability and superiority of the isogeometric analysis method were verified in optimizing the shape of the problem subject to deformation-dependent loads.