EasyPBC is an ABAQUS CAE plugin developed to estimate the homogenised effective elastic properties of user created periodic representative volume element (RVE), all within ABAQUS without the need to use third-party software. The plugin automatically applies the concepts of the periodic RVE homogenisation method in the software's user interface by categorising, creating, and linking sets necessary for achieving deformable periodic boundary surfaces, which can distort and no longer remain plane. Additionally, it allows the user to benefit from finite element analysis data within ABAQUS CAE interface after calculating homogenised properties. In this article, the algorithm of the plugin based on periodic RVE homogenisation method is explained, which could be developed for other commercial FE software packages. Furthermore, examples of its implementation and verification are illustrated.

This paper introduces a new approach to multiscale optimization, where design optimization is applied at two scales: the macroscale, where the structure is optimized, and the microscale, where the material is optimized. Thus, structure and material are optimized simultaneously. We approach multiscale design optimization by linearizing and formulating a new way to decompose into macro and microscale design problems in such a way that solving the decomposed problems separately lead to an overall optimum solution. In addition, the macro and microstructural designs are coupled tightly through homogenization and inverse homogenization. This approach is generic in that it allows any number of unique microstructures and can be applied to a wide range of design problems. An advantage of decomposing the problem in this physical way is that it is potentially straight forward to specify additional design requirements at a specific scale or in specific regions of the design domain. The decomposition approach also allows an easy parallelization of the computational methodology and this enables the computational time to be maintained at a practical level. We demonstrate the proposed approach using the level-set topology optimization at both scales, i.e. macrostructural topological design and microstructural topology of architected material. A series of optimization problems, minimizing compliance and compliant mechanism are solved for verification and investigation of potential benefits.

Uncertainty is an important consideration in structural design and optimization to produce robust and reliable solutions. This paper introduces an efficient and accurate approach to robust structural topology optimization. The objective is to minimize expected compliance with uncertainty in loading magnitude and applied direction, where uncertainties are assumed normally distributed and statistically independent. This new approach is analogous to a multiple load case problem where load cases and weights are derived analytically to accurately and efficiently compute expected compliance and sensitivities. Illustrative examples using a level set based topology optimization method are then used to demonstrate the proposed approach. Nomenclature

Robust topology optimization has long been considered computationally intractable as it combines two highly expensive computational strategies. This paper considers simultaneous minimization of expectancy and variance of compliance in the presence of uncertainties in loading magnitude, using exact formulations and analytically derived sensitivities. It shows that only a few additional load cases are required, which scales in polynomial time with the number of uncertain load cases. The approach is implemented using the level set topology optimization method. Shape sensitivities are derived using the adjoint method. Several examples are used to investigate the effect of including variance in robust compliance optimization. λ = Lagrange multiplier µ i = mean magnitude of uncertain load i σ i = standard deviation of uncertain load i € σ = covariance Ω = design domain Ω S = structural domain

This paper introduces an approach to level-set topology optimization that can handle multiple constraints and simultaneously optimize non-level-set design variables. The key features of the new method are discretized boundary integrals to estimate function changes and the formulation of an optimization sub-problem to attain the velocity function. The sub-problem is solved using sequential linear programming (SLP) and the new method is called the SLP level-set method. The new approach is developed in the context of the Hamilton-Jacobi type level-set method, where shape derivatives are employed to optimize a structure represented by an implicit level-set function. This approach is sometimes referred to as the conventional level-set method. The SLP level-set method is demonstrated via a range of problems that include volume, compliance, eigenvalue and displacement constraints and simultaneous optimization of nonlevel-set design variables.

SUMMARYLinear buckling constraints are important in structural topology optimization for obtaining designs that can support the required loads without failure. During the optimization process, the critical buckling eigenmode can change; this poses a challenge to gradient-based optimization and can require the computation of a large number of linear buckling eigenmodes. This is potentially both computationally difficult to achieve and prohibitively expensive. In this paper, we motivate the need for a large number of linear buckling modes and show how several features of the block Jacobi conjugate gradient (BJCG) eigenvalue method, including optimal shift estimates, the reuse of eigenvectors, adaptive eigenvector tolerances and multiple shifts, can be used to efficiently and robustly compute a large number of buckling eigenmodes. This paper also introduces linear buckling constraints for level-set topology optimization. In our approach, the velocity function is defined as a weighted sum of the shape sensitivities for the objective and constraint functions. The weights are found by solving an optimization sub-problem to reduce the mass while maintaining feasibility of the buckling constraints. The effectiveness of this approach in combination with the BJCG method is demonstrated using a 3D optimization problem.

Several topology optimization problems are conducted within the ribs and spars of a wing box. It is desired to locate the best position of lightening holes, truss/cross-bracing, etc. A variety of aeroelastic metrics are isolated for each of these problems: elastic wing compliance under trim loads and taxi loads, stress distribution, and crushing loads. Aileron effectiveness under a constant roll rate is considered, as are dynamic metrics: natural vibration frequency and flutter. This approach helps uncover the relationship between topology and aeroelasticity in subsonic transport wings, and can therefore aid in understanding the complex aircraft design process which must eventually consider all these metrics and load cases simultaneously.

Boundary based structural optimization methods often employ a fixed grid FEM to compute sensitivities for efficiency and simplicity. A simple and popular fixed grid approach is to modify the stiffness of elements intersected by the boundary by an areafraction weighting. However, poor sensitivities and numerical instabilities can occur when using this method. Sensitivity computation for a compliance objective is investigated and the results are used to develop a weighted least squares scheme to improve sensitivities computed by the area-fraction approach. This is implemented together with a numerically stable structural topology optimization using the level set method with no additional filtering or regularization. The performance of the proposed scheme is demonstrated by classic benchmark examples of topology optimization.