Peter D. Dunning

Introducing Loading Uncertainty in Topology Optimization

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.

Robust Topology Optimization: Minimization of Expected and Variance of Compliance

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.

Optimal Topology of Aircraft Rib and Spar Structures Under Aeroelastic Loads

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 that must eventually consider all these metrics and load cases simultaneously.

Engineering design optimization using services and workflows

Multi-disciplinary design optimization (MDO) is the process whereby the often conflicting requirements of the different disciplines to the engineering design process attempts to converge upon a description that represents an acceptable compromise in the design space. We present a simple demonstrator of a flexible workflow framework for engineering design optimization using an e-Science tool. This paper provides a concise introduction to MDO, complemented by a summary of the related tools and techniques developed under the umbrella of the UK e-Science programme that we have explored in support of the engineering process. The main contributions of this paper are: (i) a description of the optimization workflow that has been developed in the Taverna workbench, (ii) a demonstrator of a structural optimization process with a range of tool options using common benchmark problems, (iii) some reflections on the experience of software engineering meeting mechanical engineering, and (iv) an indicative discussion on the feasibility of a ‘plug-and-play’ engineering environment for analysis and design.

Aerostructural Level Set Topology Optimization for a Common Research Model Wing

The purpose of this work is to use level set topology optimization to improve the design of a representative wing box structure for the NASA common research model. The objective is to minimize the total compliance of the structure under aerodynamic and body force loading, where the aerodynamic loading is coupled to the structural deformation. A taxi bump case was also considered, where only body force loads were applied. The trim condition that aerodynamic lift must balance the total weight of the aircraft is enforced by allowing the root angle of attack to change. The level set optimization method is implemented on an unstructured three-dimensional grid, so that the method can optimize a wing box with arbitrary geometry. Fast matching and upwind schemes are developed for an unstructured grid, which make the level set method robust and efficient. The adjoint method is used to obtain the coupled shape sensitivities required to perform aerostructural optimization of the wing box structure.

Level-Set Topology Optimization with Aeroelastic Constraints

Level-set topology optimization is used to design a wing considering skin buckling under static aeroelastic trim loading, as well as dynamic aeroelastic stability (flutter). The level-set function is defined over the entire 3D volume of a transport aircraft wing box. Therefore, the approach is not limited by any predefined structure and can explore novel configurations. The Sequential Linear Programming (SLP) level-set method is used to solve the constrained optimization problems. The proposed method is demonstrated using three problems with mass, linear buckling and flutter objective and/or constraints. A constraint aggregation method is used to handle multiple buckling constraints in the wing skins. A continuous flutter constraint formulation is used to handle difficulties arising from discontinuities in the design space caused by a switching of the critical flutter mode.

Simultaneous optimisation of structural topology and material grading using level set method

Abstract The present paper introduces a new technique for simultaneously optimising the topology and continuous material distribution of a structure. Topology optimisation offers great potential for novel, improved structural designs and is an ideal design tool for additive manufacturing (AM) techniques. Level set based topology optimisation produces solutions with clear, smooth boundaries that can be directly fabricated using AM. Further benefits of AM may be realised by also optimising the material distribution within the structure. The sequential linear programming level set method is used to include material distribution design variables in the topology optimisation problem. This allows the topology and continuous material distribution to be optimised simultaneously. Several compliance minimisation problems are used to demonstrate the proposed approach.

Introducing uncertainty in direction of loading for topology optimization

Uncertainty is an important consideration in structural design and optimization to produce robust and reliable solutions. Existing methods that include loading direction uncertainty in structural topology optimization may not represent realistic uncertainties or employ a discrete sampling approach that approximates the effect of the uncertainty. The sampling approach can become computationally expensive when an accurate approximation is required. An efficient and accurate approach is developed in this paper when solving the minimization of expected compliance problem with uncertain direction of applied loading. This new approach is analogous to a multiple load case problem where load cases and weights are derived explicitly to compute exactly the expected compliance and sensitivities. The approach is then broadened to include uncertainty in magnitude of loading without penalizing efficiency. Illustrative examples using a level set based topology optimization method are then used to demonstrate the proposed approach.

Loading Magnitude Uncertainty in Level-Set Based Topology Optimization

Engineering environments are often complex, which introduces uncertainty into the design process. Thus, uncertainties should be considered during design and optimization of structures to produce robust and reliable solutions. This paper presents topology optimization with uncertainty by minimizing expected compliance. A simple and efficient formulation is developed to solve this problem under uncertainty in loading magnitude. The formulation is applied to the level set method and illustrative examples demonstrate that more robust structures can be obtained compared to the deterministic solutions.

Development of an ABAQUS plugin tool for periodic RVE homogenisation

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.