Multi-material topology optimization of structures using peridynamics

This study presents a multi-material topology optimization based on Peridynamics (PD). The conventional topology optimization mainly used a mesh-based numerical method, i.e., Finite Element (FE) method. Moving boundaries, large deformations, and cracks/damages are some limitations of the mesh-based numerical method. In this study, PD as a meshless method is proposed to employ in the topology optimization to remove limitations of the mesh-based topology optimization. The minimization of compliance, i.e., strain energy, is chosen as the objective function subjected to the volume constraint. The design variables are the relative density of the candidate materials defined at particles employing gradient based optimization approach. A filtering scheme is also adopted to avoid the checkerboard issue and maintain the optimization stability. The proposed approach is an alternative and powerful tool for multiple additive manufacturing in finding multi material optimal topologies of the structures with embedded crack

Topology optimization of cracked structures using peridynamics

Finite element method (FEM) is commonly used with topology optimization algorithms to determine optimum topology of load bearing structures. However, it may possess various difficulties and limitations for handling the problems with moving boundaries, large deformations, and cracks/damages. To remove limitations of the mesh-based topology optimization, this study presents a robust and accurate approach based on the innovative coupling of Peridynamics (PD) (a meshless method) and topology optimization (TO), abbreviated as PD-TO. The minimization of compliance, i.e., strain energy, is chosen as the objective function subjected to the volume constraint. The design variable is the relative density defined at each particle employing bi-directional evolutionary optimization approach. A filtering scheme is also adopted to avoid the checkerboard issue and maintain the optimization stability. To present the capability, efficiency and accuracy of the PD-TO approach, various challenging optimization problems with and without defects (cracks) are solved under different boundary conditions. The results are extensively compared and validated with those obtained by element free Galerkin method and FEM. The main advantage of the PD-TO methodology is its ability to handle topology optimization problems of cracked structures without requiring complex treatments for mesh connectivity. Hence, it can be an alternative and powerful tool in finding optimal topologies that can circumvent crack propagation and growth in two and three dimensional structures

Buckling Optimization of Variable Stiffness Composite Panels for Curvilinear Fibers and Grid Stiffeners

Automated Fiber Placement (AFP) machines can manufacture composite panels with curvilinear fibers. In this article, the critical buckling load of grid-stiffened curvilinear fiber composite panels is maximized using a genetic algorithm. The skin is composed of layers in which the fiber orientation varies along one spatial direction. The design variables are the fiber orientation of the panel for each layer and the stiffener layout. Manufacturing constraints in terms of maximum curvature allowable by the AFP machine are imposed for both skin and stiffener fibers. The effect of manufacturing-induced gaps in the laminates is also incorporated. The finite element method is used to perform the buckling analyses. The panels are subjected to in-plane compressive and shear loads under several boundary conditions. Optimization results show that the percentage difference in the buckling load between curvilinear and straight fiber panels depends on the load case and boundary conditions

Dynamic Scaling of a Wing Structure Model Using Topology Optimization

In this paper, a dynamic scaling methodology is introduced to devise reduced scaled models of aircraft with the objectives of minimizing the development cost and exploring the design space. A promising way to accomplish this is using Topology Optimization (TO) for Additive Manufacturing (AM). Here, TO is employed to design a reduce scale model by matching its natural frequencies and mode shapes to those of a full scale model. Different TO strategies based on density approach are tested with the goal of achieving a dynamically scaled structure that can be manufactured. To achieve this goal, the TO solution should be free from intermediate densities, which is observed for some TO strategies but not all. When no penalization factor is applied: (i) the relative difference between natural frequencies is less than 1% and (ii) the estimated Modal Assurance Criteria (MAC) metric to evaluate the correlation between mode shapes is close to the ideal identity matrix. These results demonstrate the effectiveness of the dynamic scaling methodology. However, when using a penalization factor to avoid intermediate densities, the dynamic behavior correlation between full and scaled models degrades. This trend is more visible in the MAC metric, where off-diagonal terms above 20% and diagonal terms below 90% appear

Multi-material topology optimization of structures with discontinuities using peridynamics

This study proposes an approach for solving density-based multi-material topology optimization of cracked structures using Peridynamics. The alternating active-phase algorithm is utilized to transform the multi-material problem into a series of binary phase topology optimization sub-problems. Instead of the conventional mesh-based methods, the Peridynamics theory (PD) is used as a tool to model the behaviour of the materials and solve for the displacement field. The most significant advantage of PD is its ability to model discontinuities in a relatively straightforward manner. Thus, in the present work, the effect of cracks as a discontinuity is investigated on the optimal multi-material topologies. The Solid Isotropic Material with Penalty (SIMP) method is utilized to define the material properties as a function of the design variables. Also, the optimization problem is solved through the Optimality Criteria (OC) approach. The proposed method is compared to the results reported in the literature by executing three numerical examples that investigate the effect of the direction of an interior crack on the optimal topologies. Moreover, the efficiency of the proposed approach is verified by solving several examples where we aim at minimizing the compliance of the structure with and without initial crack

Dynamic Scaling of a Wing Structure Model Using Topology Optimization

In this paper, a dynamic scaling methodology is introduced to devise reduced scaled models of aircraft with the objectives of minimizing the development cost and exploring the design space. A promising way to accomplish this is using Topology Optimization (TO) for Additive Manufacturing (AM). Here, TO is employed to design a reduce scale model by matching its natural frequencies and mode shapes to those of a full scale model. Different TO strategies based on density approach are tested with the goal of achieving a dynamically scaled structure that can be manufactured. To achieve this goal, the TO solution should be free from intermediate densities, which is observed for some TO strategies but not all. When no penalization factor is applied: (i) the relative difference between natural frequencies is less than 1% and (ii) the estimated Modal Assurance Criteria (MAC) metric to evaluate the correlation between mode shapes is close to the ideal identity matrix. These results demonstrate the effectiveness of the dynamic scaling methodology. However, when using a penalization factor to avoid intermediate densities, the dynamic behavior correlation between full and scaled models degrades. This trend is more visible in the MAC metric, where off-diagonal terms above 20% and diagonal terms below 90% appear