Harnessing Structural Optimization Techniques for Developing Efficient Light-Weight Vehicles

<div class="htmlview paragraph">In various practical structural design problems, decision of a layout of material or stiffeners in the given design space satisfying some design constraints is the most difficult task for design engineers. Also, they must consider many possible cases for safety, performance and some other requirements. But it is very difficult to solve this type of layout (topology) problem by any conventional structural optimization techniques because its mathematical modeling of topology is so complex. To solve this problem, we employed the new topology optimization technique using the homogenization method that was recently introduced by Bensøe and Kikuchi. The method gives the minimum compliance design under certain material constraint. This technique was also extended to three dimensional shells and three dimensional solids by Suzuki and Kikuchi.</div> <div class="htmlview paragraph">In this paper, shape and topology optimization problem under multi-loading conditions is discussed. Various car body design problems are solved to justify the validity and the strength of the present approach for engineering applications.</div>

During the last 20 years, structural optimization has become one of the most important topics of engineering applications. Design optimization of structure has been an interesting area of research in the field of engineering design for its ability to short the design cycle and to enhance product quality. Significant research activity has occurred in the area of structural optimization in the last decade. Especially for topology optimization of structure, many new theoretical, algorithmic, and computational contributions have resulted by researchers and engineers. Topology optimization is a powerful tool for global and multi-scale design of macrostructures, microstructures, and the cell of prescribed composite materials. The population based evolutionary algorithms have emerged as powerful mechanism for finding optimum solutions of complex optimization problems in engineering during the last two decades. Evolutionary computation is the study of computational systems which use ideas and get inspiration from natural evolution and adaptation [1]. The thinking has wide application in various engineering fields, such as computer science, artificial intelligence, operations research. Genetic algorithm is another kind of bio-inspired optimization method and it is playing an increasingly important role in studies of complex adaptive systems. Its application ranges from adaptive agents in economic theory to the use of machine learning techniques in the design of complex devices and structures, such as aircraft turbines and integrated circuits [2]. Optimization of structures can be classified into three categories: sizing, shaping, and topology optimization. In the topology optimization, it is concerned with the structure members and connectivity between members. In general, it is easily represented by discrete variables rather than by those used for continuous optimization problems. Topology optimization is the most difficult and complex among three categories and it is special useful in developing innovative conceptual designs. Structural optimization, in particular the topology optimization, has been identified as one of the most challenging tasks in structural design. Various techniques and approaches have been established during the last two decades. Topology optimization usually referred to as layout optimization or general shape optimization [3]. It lets engineers get the optimal topology of structure or new configurations during product design phase, as they are implementing the design of the size

<div class="section abstract"><div class="htmlview paragraph">This paper presents the design, structural analysis, structural test validation and risk assessment done by Cummins to evaluate the structural integrity of Light Duty engine cylinder head for a Medium Wheelbase (MWB) pick-up truck. Initially, Cummins used the 2.5L and 3.0L (4-cylinder) engines that have standard power ratings based on existing requirements, but rising market demands for more power, fuel efficiency, lower cost and weight, and future emission compliance led to customer requirements for 15% uprate for 2.5L and 22% uprate for 3.0L from the same base engine. The increase in power requirement possesses challenges on critical components, especially cylinder heads in terms of thermal and structural limits.</div><div class="htmlview paragraph">Multiple analysis led design iterations were performed using cutting edge CAE software such as Ansys, Dassault Systems fe-safe, and PTC Creo to ensure the structural integrity of the cylinder head under high thermal and mechanical loads, and to keep design margins within acceptable limits. A key feature identified through topology optimization was diagonal ribbing pattern on each cylinder, which is novel, and similar pattern can be applied to both new and existing engine platforms to enhance stiffness without major changes to the water jacket.</div><div class="htmlview paragraph">The Cylinder head was subjected to a long endurance test, which comprises of high thermal and mechanical loads under extreme operating conditions. After running for specified number of hours as per inhouse test requirements, the engine was stopped for magnetic particle inspection for any signs of fatigue failure.</div><div class="htmlview paragraph">No major cracks were observed on the 3.0L Cylinder head combustion face. However, a few cracks were observed on the 2.5L cylinder head combustion face at exhaust & intake bridges. Upon investigation, it was concluded that crack was due to high thermo-mechanical fatigue loads and hence further optimization was carried out on the cylinder head design. Furthermore, cylinder head gasket coolant orifice optimization is done to improve the coolant distribution to each cylinder. Thermal analysis showed a reduction in exhaust & intake bridge temperature within the acceptable limits. This paper captures the detailed design and structural analysis on 3.0L and 2.5 L diesel engine Cylinder head.</div></div>

Structural topology optimization.- On basic properties of Michell's structures.- Validation of numerical method by analytical benchmarks and verification of exact solutions by numerical methods.- Introduction to shape and topology optimization.- Homogenization method for shape and topology optimization.- Level set method for shape and topology optimization.- Compliance minimization of two-material elastic structures.- Some notes on topology optimization of vibrating continuum structures.- Topology optimization of vibrating continuum structures for maximum values of simple and multiple eigenfrequencies and frequency gaps.- On optimum shape design and periodicity of band-gape beam structures.- Topological design for minimum dynamic compliance of continuum structures subjected to forced vibration.- Topological design for minimum sound emission from bi-material structures subjected to forced vibration.- Discrete material optimization of vibrating laminated composite plates for minimum sound emission.- Optimization of diffusive transport problems.- Fluid topology optimization: stokes and Navier-stokes models.- Topology optimization of coupled multi-physics problems.- Topology optimization based on the extended finite element method.- Topology optimization of meso- and nano-scale problems.- Topology optimization under uncertainty.- A brief review of numerical methods of structural topology optimization.- The free material design in planar elasticity.

This article proposes an efficient parameterized level set method (PLSM) for structural topology optimization design with minimum compliance as the objective function and volume fraction as the constraint condition. In the stage of establishing the optimization model, the level set function (LSF) is interpolated using compactly-supported radial basis functions (CS-RBFs) to transform the Hamilton-Jacobi partial differential equation (PDE) into ordinary differential equations (ODEs), thereby making the evolution of the LSF more convenient and efficient, and ensuring the smoothness of the optimization result boundary. The method of moving asymptotes (MMA) is used for solving the established optimization model, and meanwhile the shape sensitivity constraint factor is added to improve computational efficiency. During the evolution of the LSF, an approximate re-initialization scheme is employed to prevent the gradient of the LSF boundary from being too large or too small, thereby improving the numerical stability and the convergence speed of structural topology optimization process. Furthermore, the proposed method is also extensible and applicable to topology optimization of multi-material structures. The feasibility and effectiveness of this method have been verified through several typical numerical examples involving topology optimization of single-material structures and multi-material structures within the framework of minimum compliance design. HIGHLIGHTS An efficient parameterized level set method using the approximate re-initialization scheme is proposed for structural topology optimization. The approximate re-initialization scheme is employed when solving the parameterized level set function via the MMA algorithm. This scheme can prevents the gradient of the level set function boundary from being too large or too small, making the level set function update more stable and accelerating the convergence speed of structural topology optimization. The effectiveness and feasibility of the proposed method are demonstrated through examples of single-material and multi-material structural topology optimization.

<div class="htmlview paragraph">The impact of structural optimization is growing in many industries due to economic pressures demanding efficiency in the design process. This efficiency implies developing products which are cost effective and ahead of the competition at the same time. The motivation of the present work is to provide the structural design engineer with tools of optimization techniques and practices that have been applied successfully to landing gears.</div> <div class="htmlview paragraph">Modern landing gears have to meet a multitude of landing and ground handling design loads whose magnitudes are several times the gross weight of the aircraft. All the design loads have to be investigated and their effect on each component must be evaluated. Furthermore, the response of the landing gears to all the design loads must be constrained to satisfy the design requirements while minimizing its structural weight. The weight of the landing gear is becoming an ever more important factor, as inefficient design can add unnecessary weight to the aircraft and, consequently, decrease the payload or useful load.</div> <div class="htmlview paragraph">Typical design examples of components of landing gears are presented that demonstrate the performance of STARSTRUC as an effective weight optimization design tool. The minimum weight design is achieved when the landing gear is subjected to behavior constraints on stresses, deflections, buckling, and frequencies of vibration.</div>

Topology optimization (TO) is currently a focal point for researchers in the field of structural optimization, with most studies concentrating on single-loading conditions. However, real engineering structures often have to work under various loading conditions. Approaches addressing multiple-loading conditions often necessitate subjective input in order to determine the importance of each loading condition, aiming for a compromise between them. This paper proposes a so-called bisection constraint method (BCM), offering a unique, user-preference-independent solution for TO problems amidst multiple-loading conditions. It is well-known that minimizing the system’s compliance is commonly used in TO as the objective. Generally, compliance is not as sufficient as stress to be used as a response to evaluate the performance of structures. However, formulations focusing on minimizing stress levels usually pose significant difficulties and instabilities. On the other hand, the compliance approach is generally simpler and more capable of providing relatively sturdy designs. Hence, the formulation of min–max compliance is used as the target problem formulation of the proposed method. This method attempts to minimize compliance under only one loading condition while compliances under the remaining loading conditions are constrained. During the optimization process, the optimization problem is automatically reformulated with a new objective function and a new set of constraint functions. The role of compliance under different loading conditions, i.e., whether it is to be treated as an objective or constraint function, might be changed throughout the optimization process until convergence. Several examples based on the solid isotropic material with penalization (SIMP) approach were conducted to illustrate the validity of the proposed method. Furthermore, the general effectiveness of the compliance approach in terms of stress levels is also discussed. The calculation results demonstrated that while the compliance approach is effective in several cases, it proves ineffective in certain scenarios.

This thesis aims at understanding and improving topology optimization techniques focusing on density-based level-set methods and geometrical nonlinearities. Central in this work are the numerical modeling of the mechanical response of a design and the consistency of the optimization process itself. Concerning the first topic, we investigate different means to improve the robustness of density-based numerical models including geometrical nonlinearities. The conventional approach (scaling the local material properties) can result in convergence problems due to excessive deformation in low-stiffness finite elements. To avoid excessive deformation, we combine the element connectivity parameterization method (adapting the connectivity between finite elements) with level-set-based topology optimization. Furthermore, we achieve greater robustness of analysis method using a second and improved approach called element deformation scaling. This approach eliminates the need for solving internal equilibrium equations (needed for the element connectivity parameterization method) via an explicit relation between the local internal and global external displacement field. The second focus of this thesis is on the optimization process of level-set-based topology optimization, and in particular its numerical consistency. We observe that signed-distance reinitialization of the level-set function affects the shape of a design in the optimization process. To minimize this effect, we propose a discrete level-set method that is based on an approximate Heaviside function and focusing on the implementation. Furthermore, we also propose a level-set-based topology optimization method using an exact Heaviside function and mathematical programming that effectively eliminates the need for reinitialization. We demonstrate that our density-based level-set method is closely related to conventional density-based topology optimization methods, while offering the advantage of more control over the geometrical complexity. On the other hand, we confirm that the dependence of the final result on the initial design which remains one of the big challenges for level-set-based topology optimization. The potential of the proposed level-set method is shown by applying it on problems with stress constraints and geometrical nonlinearities and performing manufacturing tolerant topology optimization. Finally, this thesis offers a review of level-set methods for structural topology optimization to identify and discuss the different approaches that are available in literature. We can distinguish between level-set methods by examination of their design parameterization, sensitivities, update procedures and regularization techniques. A level-set-based design parameterization offers the advantage of a crisp distinction between subdomains. For this reason, X-FEM approaches and conforming discretizations are an interesting option to retain the crisp nature of the level-set-based description of the design. Many level-set methods are combined with density-based numerical models and are, therefore, closely related to conventional density-based topology optimization methods. In particular, recently proposed projection methods have much in common with a level-set-based design description. The results of level-set-based TO methods often rely heavily on regularization techniques that introduce inconsistencies in the optimization process. Numerical consistency does not necessarily lead to the best search direction, but is essential to find a Karush-Kuhn-Tucker point of the discretized optimization problem.

This paper presents a numerical analysis technique for shape optimization of linear elastic structures subject to multiple loading conditions. The technique presented here is based on the traction method for determining the domain variation that reduces the objective functional. Using the speed method, a volume minimization problem is formulated in which the mean compliances associated with individual load cases act as constraints. The shape gradient function, which is equivalent to the shape sensitivity, for this problem is obtained using the Lagrange multiplier method. With the traction method, the domain variation is numerically analyzed using a commercial FEM code. A method is also proposed for finding the domain variation so as to satisfy equality and inequality constraints. The analytical results show the effectiveness and practical utility of the proposed method in solving shape optimization problems involving multiple loading conditions.

Stress-based topology optimization and nonlinear structural topology optimization is gaining increasing attention in order to make topology optimization more realistic. Thus, this paper extends current concepts of topology optimization to the design of structures made of nonlinear materials. An extended bi-directional evolutionary structural optimization (BESO) method for stress minimization topology optimization of material nonlinear structures is proposed in this work. BESO method based on discrete variables can effectively avoid the well-known singularity problem in density-based methods with low-density elements. The maximum von Mises stress is approximated by the p-norm global stress. The sensitivity information for designing variable updates is derived in detail by adjoint method. As for the highly nonlinear stress behavior, the updated scheme takes advantages from two filters respectively of the sensitivity and topological variables to improve convergence. Moreover, the filtered sensitivity numbers are combined with their historical sensitivity information to further stabilize the optimization process. The effectiveness of the proposed method is demonstrated by several 2D benchmark design problems.

Smoothing topology optimization results using pre-built lookup tables

<div class="section abstract"><div class="htmlview paragraph">The availability of new technologies and the growing interest in the development of autonomous aircraft has created a demand for performance evaluation of aircraft flying at high altitudes over a long period of time for applications such as monitoring, telecommunications, etc. This work presents a study on the use of wings with high aspect ratio for the application in unmanned aircraft, that fly at high altitudes and require great endurance to remain flying as long as possible. With reference to the AeroVironment Helios aircraft, which hit the altitude record in 2001, flying at more than 29,000 meters altitude, a comparison was made between five wings with different wingspan from the aerodynamic and structural point of view. The aerodynamic performance of each wing was calculated and structural design and sizing was performed, assuming that it is the main structural component of the wing. Optimazing each wing aerodynamically and structurally, it was possible to compare wing performance in terms of maximum range and maximum endurance. The analysis focused on evaluate the aerodynamic and structural performance for a more efficient design that meets flight requirements. The results showed that the increase in wingspan improves the aerodynamic performance of the wing, but with the cost of increasing its structural weight. The wing with the largest wingspan (20% increase relative to the baseline wing), although presented the best aerodynamic characteristics, presented bad performance due to its heavy weight. However, the proposed modification of the original wing with 10% increase in wingspan presented the best performance in terms of range and endurance.</div></div>

<div class="section abstract"><div class="htmlview paragraph">Topology optimization (TO) represents an invaluable instrument for the structural design of components, with extensive use in numerous industries including automotive and aerospace. TO allows designers to generate lightweight, non-intuitive solutions that often improve overall system performance. Utilization of multiple materials within TO expands its range of applications, granting additional freedom and structural performance to designers. Often, use of multiple materials in TO results in material placement that may not have been previously identified as optimal, providing designers with the ability to produce novel high performance systems. As numerous modern engineering materials possess anisotropic properties, a logical extension of multi-material TO is to include provisions for anisotropic materials. Herein lies the focus of this work.</div><div class="htmlview paragraph">A TO algorithm capable of considering anisotropic material properties is used to investigate a case study on the design of an automotive hood panel. A baseline aluminum hood panel is used to generate stiffness targets for optimization, followed by the generation of a design space model to allow the algorithm to determine optimal material placement. Optimization is undertaken with two types of AS4 continuous carbon fiber reinforced epoxy, each in two orientations. Optimal hood panel solutions that maintain stiffness levels of the conventional baseline are achieved. The mass of the design space is minimized, and constrained through the baseline displacement values. The effect of hood panel thickness and offset distance between panel layers is also investigated.</div><div class="htmlview paragraph">The optimal topologies indicated an overall mass savings of up to 44.5% in relation to the baseline, while maintaining hood panel stiffness. Comparative mass savings decreased as hood panel thickness increased and offset distance decreased. The allocation of stiffer materials was observed near locations of applied loads and constraints, with highly anisotropic materials placed along hood panel extremities. The practicality of anisotropic multi-material TO in lightweight design was thus demonstrated.</div></div>

Reinforced concrete (RC) frames are extensively used in construction of buildings worldwide. The conventional design of these buildings typically relies on a "trial and error" method, starting with initial dimensioning followed by validation of the preliminary design. This approach makes it difficult to calculate potential cost savings in materials, while maintaining structural safety. In recent decades, the need for more efficient, safe and rational seismic design procedures has led to an increasing interest in structural optimisation of RC frames. However, due to the complex non-linear behaviour of RC frames, arriving at their optimum design under earthquake excitations is challenging. Even at serviceability limit state, concrete cracking can lead to significant stiffness changes and redistribution of inertial forces, phenomena that are normally expected after steel yielding. To mitigate these drawbacks, numerous combinations of section dimensions and reinforcement arrangements can be considered as design variables during a structural size optimisation process. However, this is seldom done for RC frames, as it requires seismic analyses with a high level of accuracy, which can be computationally expensive. Meanwhile, design optimisation has been identified as a feasible way to reduced embodied carbon emissions in construction, and therefore, a change of design paradigms is necessary. The article aims to critically review the major developments in recent seismic design optimisation studies on RC buildings, focusing on structural size optimisation, with the goal of identifying the main achievements and limitations. Different design objectives in current seismic design optimisation procedures are first summarised. The key steps in structural optimisation are then discussed, including design variables, design constraints, application of optimization methodologies, and evaluation of seismic performance. Finally, the research gaps in this field are identified, and suggestions are provided for future research directions. This article contributes towards the development of more efficient seismic design methods for RC structures, which in turn can lead to more sustainable construction.

<div class="section abstract"><div class="htmlview paragraph">The design of drive units in electric vehicles (EVs) presents challenges due to the need to pass multiple linear and non-linear load cases. This can result in inefficient design. Therefore, optimization plays a critical role in improving the design efficiency. However, setting up the optimization process itself can be challenging, especially when dealing with complex design variables and different load cases that require the use of various computer-aided engineering (CAE) solvers. The drive unit, being a casting component, presents additional challenges in setting up Multidisciplinary Design Optimization (MDO) process. This paper introduces an efficient process for addressing these challenges by presenting a sample Multidisciplinary Design Optimization (MDO) problem. The problem involves the manipulation of discrete design variables, such as the number of ribs, and incorporates five different load cases that require the utilization of different CAE solvers. The proposed process demonstrates a streamlined approach that can be completed in less than one week. It showcases the steps involved in setting up the optimization process, including defining the design variables, selecting appropriate load cases, and integrating different CAE solvers. By following this process, engineers can effectively optimize the design of drive units in EVs, leading to improved mass efficiency. Overall, this paper highlights the importance of optimization in addressing the challenges associated with the design of drive units in EVs. It presents a practical and efficient process that can be implemented within a short timeframe, allowing engineers to achieve optimal design solutions. By leveraging this approach, manufacturers can enhance the performance and efficiency of EV drive units, contributing to the advancement of electric mobility.</div></div>