• Steel and Composite Structures
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• v.46 no.1
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• pp.33-51
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• 2023

This research presents a multi-material topology optimization for functionally graded material (FGM) and nonFGM with elastic buckling criteria. The elastic buckling based multi-material topology optimization of functionally graded steels (FGSs) uses a Jacobi scheme and a Method of Moving Asymptotes (MMA) as an expansion to revise the design variables shown first. Moreover, mathematical expressions for modified interpolation materials in the buckling framework are also described in detail. A Solid Isotropic Material with Penalization (SIMP) as well as a modified penalizing material model is utilized. Based on this investigation on the buckling constraint with homogenization material properties, this method for determining optimal shape is presented under buckling constraint parameters with non-homogenization material properties. For optimal problems, minimizing structural compliance like as an objective function is related to a given material volume and a buckling load factor. In this study, conflicts between structural stiffness and stability which cause an unfavorable effect on the performance of existing optimization procedures are reduced. A few structural design features illustrate the effectiveness and adjustability of an approach and provide some ideas for further expansions.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.15 no.7
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• pp.4087-4092
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• 2014

The gangway connection of the articulated high speed railway vehicles (HSRV) is a double wrinkled rubber component to seal the air of the corridor under a range of angular deviations between the carriage end parts. From the results of non-linear structural analysis, one of the severe loading conditions for the connection is mixed mode (rolling+yawing) angular displacements while passing through the small-radius curved siding track of the HSRV depot. In this study, to ensure the safety enhancement of the component, the optimal design for the cross section of that was performed using the Solid Isotropic Material with Penalization (SIMP) method. Nonlinear finite element analysis confirmed that the decreases in the maximum principal strain of the optimized design under rolling and mixed modes are 68% and 39%, respectively, compared to the initial design.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.30 no.10 s.253
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• pp.1187-1193
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• 2006

Traditionally, the continuum-based topology optimization methods employing the SIMP technique have been used to design compliant mechanisms. Although they have been successful, the optimized mechanisms by the methods are usually difficult to manufacture because of their geometrical complexities. The objective of this study is to develop a topology optimization method that can produce easy-to-fabricate mechanism structure. The proposed method is a ground beam method where beam connectivity is controlled by the beam joint stiffness. In this approach, beam joint stiffness determines the mechanism configuration. Because b the ground structure beams have uniform thicknesses varying only discretely, the resulting mechanism topologies become easily manufacturable.

• Steel and Composite Structures
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• v.27 no.1
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• pp.27-33
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• 2018

In this study, a mixed-interpolated tensorial component 4 nodes method (MITC4) is treated as a numerical analysis model for topology optimization using multiple materials assigned within Reissner-Mindlin plates. Multi-material optimal topology and shape are produced as alternative plate retrofit designs to provide reasonable material assignments based on stress distributions. Element density distribution contours of mixing multiple material densities are linked to Solid Isotropic Material with Penalization (SIMP) as a design model. Mathematical formulation of multi-material topology optimization problem solving minimum compliance is an alternating active-phase algorithm with the Gauss-Seidel version as an optimization model of optimality criteria. Numerical examples illustrate the reliability and accuracy of the present design method for multi-material topology optimization with Reissner-Mindlin plates using MITC4 elements and steel materials.

• Steel and Composite Structures
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• v.51 no.2
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• pp.203-223
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• 2024

This study shows functionally graded material structural topology optimization under buckling constraints. The SIMP (Solid Isotropic Material with Penalization) material model is used and a method of moving asymptotes is also employed to update topology design variables. In this study, the quadrilateral element is applied to compute buckling load factors. Instead of artificial density properties, functionally graded materials are newly assigned to distribute optimal topology materials depending on the buckling load factors in a given design domain. Buckling load factor formulations are derived and confirmed by the resistance of functionally graded material properties. However, buckling constraints for functionally graded material topology optimization have not been dealt with in single material. Therefore, this study aims to find the minimum compliance topology optimization and the buckling load factor in designing the structures under buckling constraints and generate the functionally graded material distribution with asymmetric stiffness properties that minimize the compliance. Numerical examples verify the superiority and reliability of the present method.

• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.19 no.4
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• pp.434-439
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• 2010

A compliant mechanism is a mechanism that produces its motion by the flexibility of some or all of its members when input force or thermal load is applied. Whereas the topology optimizations based on homogenization and SIMP parameterization have been successfully applied for compliant mechanism design, ESO approach has been hardly considered yet for the optimization of these types of systems. In this paper, traditional ESO method is adopted to achieve the optimum design of a compliant mechanism for thermal load, since AESO method cannot consider the effect of both heat conduction and convection. Sensitivity number, a criterion for element removal in traditional ESO, was newly defined for input thermal loading. The procedure has been tested in numerical applications and compared with the results obtained by other methods to validate these approaches.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.34 no.3
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• pp.159-165
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• 2021

This study introduces a topology optimization method for the simultaneous design of macro-scale structural configuration and unit structure variation to ensure effective heat conduction. Shape changes in the unit structure depending on its location within the macro-scale structure result in micro- as well as macro-scale design and enable better performance than using isotropic unit structures. They result in functionally graded composite structures combining both configurations. The representative volume element (RVE) method is applied to obtain various thermal conductivity properties of the multi-material based unit structure according to its shape change. Based on the RVE analysis results, the material properties of the unit structure having a certain shape can be derived using machine learning. Macro-scale topology optimization is performed using the traditional solid isotropic material with penalization method, while the unit structures composing the macro-structure can have various shapes to improve the heat conduction performance according to the simultaneous optimization process. Numerical examples of the thermal compliance minimization issue are provided to verify the effectiveness of the proposed method.

• Smart Structures and Systems
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• v.11 no.3
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• pp.241-259
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• 2013

This paper presents the optimum load-speed diagram evaluation for a linear micromotor, including multitude cantilever piezoelectric bimorphs, briefly. Each microbeam in the mechanism can be actuated in both axial and flexural modes simultaneously. For this design, we consider quasi-static and linear conditions, and a relatively new numerical method called the smoothed finite element method (S-FEM) is introduced here. For this purpose, after finding an optimum volume fraction for piezoelectric layers through a standard numerical method such as quadratic finite element method, the relevant load-speed curves of the optimized micromotor are examined and compared by deterministic topology optimization (DTO) design. In this regard, to avoid the overly stiff behavior in FEM modeling, a numerical method known as the cell-based smoothed finite element method (CS-FEM, as a branch of S-FEM) is applied for our DTO problem. The topology optimization procedure to find the optimal design is implemented using a solid isotropic material with a penalization (SIMP) approximation and a method of moving asymptotes (MMA) optimizer. Because of the higher efficiency and accuracy of S-FEMs with respect to standard FEMs, the main micromotor characteristics of our final DTO design using a softer CS-FEM are substantially improved.

• International Journal of CAD/CAM
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• v.8 no.1
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• pp.1-10
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• 2009

This paper presents a topology optimization approach using element-free Galerkin method (EFGM) for the optimal design of compliant mechanisms with geometrically non-linearity. Meshless method has an advantage over the finite element method(FEM) because it is more capable of handling large deformation resulted from geometrical nonlinearity. Therefore, in this paper, EFGM is employed to discretize the governing equations and the bulk density field. The sensitivity analysis of the optimization problem is performed by incorporating the adjoint approach with the meshless method. The Lagrange multipliers method adjusted for imposition of both the concentrated and continuous essential boundary conditions in the EFGM is proposed in details. The optimization mathematical formulation is developed to convert the multi-criteria problem to an equivalent single-objective problem. The popularly applied interpolation scheme, solid isotropic material with penalization (SIMP), is used to indicate the dependence of material property upon on pseudo densities discretized to the integration points. A well studied numerical example has been applied to demonstrate the proposed approach works very well and the non-linear EFGM can obtain the better topologies than the linear EFGM to design large-displacement compliant mechanisms.

• Structural Engineering and Mechanics
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• v.45 no.6
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• pp.759-777
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• 2013

In this paper, a topology optimization method based on the element independent nodal density (EIND) is developed for continuum solids with multiple load cases and multiple constraints. The optimization problem is formulated ad minimizing the volume subject to displacement constraints. Nodal densities of the finite element mesh are used a the design variable. The nodal densities are interpolated into any point in the design domain by the Shepard interpolation scheme and the Heaviside function. Without using additional constraints (such ad the filtering technique), mesh-independent, checkerboard-free, distinct optimal topology can be obtained. Adopting the rational approximation for material properties (RAMP), the topology optimization procedure is implemented using a solid isotropic material with penalization (SIMP) method and a dual programming optimization algorithm. The computational efficiency is greatly improved by multithread parallel computing with OpenMP to run parallel programs for the shared-memory model of parallel computation. Finally, several examples are presented to demonstrate the effectiveness of the developed techniques.