Glass sponge-inspired ceramic graded lattices: multi-objective-driven structural optimization for mechanical design

Machine Learning User Preferences for Structural Design

A shape design sensitivity analysis and optimization procedure is proposed using a meshfree method. A CAD tool connection is established to facilitate the seamless integration of structural modeling, simulation, and design optimization. A new CAD-based method for design velocity computation is proposed, applicable to both the meshfree method and the finite element method. A shape design variable can be chosen among the geometric parameters defined in the CAD model in order to support a concurrent engineering environment. A new CAD-based method for updating the discrete model is proposed, such that the meshfree model is automatically updated in a continuous and consistent way during design optimization. The proposed method is applied to 2D and 3D linear elastic problems, as well as to a large deformation hyperelastic problem.

Structural analysis and design optimization have recently been extended to stochastic approach to take various uncertainties into account. However in areas whwew it is not possible to produce accurate statistical information, the probabilistic method is not appropriate for stochastic structural analysis and design optimization, since improper modeling of uncertainty could cause greater degree of statistical uncertainty than those of physical uncertainty. For uncertainty with insufficient information, possibility-based (or fuzzy set) methods have recently been introduced in stochastic structural analysis and design optimization. The main advantage of the fuzzy analysis is that it preserves the intrinsic random nature of physical variables through their membership functions and, when used for evaluation of designs, yields more conservative design than those from the probabilistic methods. There are two computational aspects in the fuzzy analysis compared to the probability analysis. First, the input fuzzy variables can be defined easier than the input random variables when no or very limited statistical data are available. Secondly, extended fuzzy operations are much simpler than those required to use probability, especially when a number of variables are involved. For possibility-based design optimization (PBDO), like for reliability-based design optimization (RBDO), the performance measure approach (PMA) with an inverse fuzzy analysis is more appropriate than other approaches, such as a possibility index approach. This paper proposes a new formulation of PBDO using PMA. It is also found that PBDO is more desirable than RBDO, since PBDO can inherently handle a system level possibility unlike RBDO. For the inverse fuzzy analysis, the maximal possibility search (MPS) method is proposed to improve numerical efficiency and accuracy comparing with the vertex method and the

Nowadays, the most updated CAE systems include structural optimization toolbox. This demonstrates that topological optimization is a mature technique, although it is not a well-established design practice. It can be applied to increase performance in lightweight design, but also to explore new topological arrangements. It is done through a proper definition of the problem domain, which means defining functional surfaces (interface surfaces with specific contact conditions), preliminary external lengths and geometrical conditions related to possible manufacturing constraints. In this sense, its applicability is possible for all kind of manufacturing, although, in Additive Manufacturing, its extreme solutions can be obtained. In this paper, we aim to present the general applicability of topological optimization in the design workflow together with a case study, exploited according to two design intents: the lightweight criterion and the conceptual definition of an enhanced topology. It demonstrates that this method may help to decrease the design efforts, which, especially in the case of additive manufacturing, can be reallocated for other kind of product optimization.

Multivariable optimization techniques have emerged as powerful tools in civil engineering design, enabling engineers to achieve optimal structural, environmental, and economic performance by simultaneously considering multiple conflicting objectives. This paper explores the applications of multivariable optimization methods such as gradient-based algorithms, genetic algorithms, and particle swarm optimization in the design of civil infrastructure. Key areas include structural optimization, resource allocation, cost minimization, and sustainability integration. The study highlights case examples illustrating the improvement in design efficiency, robustness, and sustainability. A comparative analysis of optimization methods is provided alongside a graphical demonstration of cost versus structural safety trade-offs. The paper concludes with a discussion on future trends and challenges in incorporating multivariable optimization for intelligent civil engineering solutions.

Structural–acoustic optimum design of shell structures in open/closed space based on a free-form optimization method

The design of reinforced concrete (RC) structures involves several kinds of uncertainties, which are usually considered through the partial safety factors prescribed in the codes of practice. The traditional design optimization of RC structures uses deterministic information of the problem. The partial safety factors are used to consider loading fluctuation and the variability of material properties. The use of these safety factors in deterministic optimization usually leads to over-designing structures, as these safety factors are calibrated for a large class of structures. In the deterministic optimization procedure the reliability cannot be controlled. For this reason, the Reliability-Based Design Optimization (RBDO) is devoted to design economical and reliable structures. However, the RBDO problem involves the evaluation of probabilistic constraints performed by the reliability analysis. The most common RBDO formulations are based on a nested optimization problem, with an outer loop for the design optimization and an inner loop for the reliability analysis. Therefore, an expensive computation effort is required to solve the RBDO problem. In this paper, a new RBDO method of RC structures is proposed. The RBDO problem is decomposed to several cycles of deterministic design optimization (DDO) based on new safety factors called Optimal System Safety Factors (OSSF). At each cycle of the DDO, the system reliability analysis is performed to verify the reliability of the optimal design, the OSSF are computed by a probabilistic method on the basis of the previous system reliability analysis, then the updated OSSF are provided for the next cycle of the DDO. The application to the design of an RC structure shows the interest and the efficiency of the proposed method.

Because of their superior mechanical, structural, and electronic properties, graphene sheets (GSs) are supposed to be components of nanoelectromechanical systems (NEMS). In this study, we carry out shape and structural optimization of GSs with topological defects in natural vibration problem to enhance their fundamental frequencies. At first, we model GSs as continuum frame models based on the molecular mechanics method. Then, we carry out shape design optimization of GSs by using a developed free-form optimization method for frame structures. In the shape design optimization, we use the fundamental frequency as objective function and enhance it considering volume constraint and repeated eigenvalues. Next, we derive the optimal atom structures of GSs with topological defects using a combination of the Phase-Field-Crystal method, the Voronoi tessellation method, and molecular dynamics simulation. The numerical results show that the fundamental frequencies of GSs can be significantly increased according to the shape and structural design optimization, and we can get their optimal atom structures with defects, which is helpful for designing GSs as components in NEMS.

Swarm intelligence hybridized with genetic search in multi-objective design optimization under constrained-Pareto dominance

A prominent advantage of using surrogate models in structural design optimization is that computational effort can be greatly reduced without significantly compromising model accuracy. The essential goal is to perform the design optimization with fewer evaluations of the typically finite element analysis and ensuring accuracy of the optimization results. An adaptive surrogate based design optimization framework is proposed, in which Latin hypercube sampling and Kriging are used to build surrogate models. Accuracy of the models is improved adaptively using an infill criterion called expected improvement (EI). It is the anticipated improvement that an interpolation point will lead to the current surrogate models. The point that will lead to the maximum EI is searched and used as infill points at each iteration. For constrained optimization problems, the surrogate of constraint is also utilized to form a constrained EI as the corresponding infill criterion. Computational trials on mathematical test functions and on a three-dimensional aircraft wing model are carried out to test the feasibility of this method. Compared with the traditional surrogate base design optimization and direct optimization methods, this method can find the optimum design with fewer evaluations of the original system model and maintain good accuracy.

To obtain reliable designs, aleatory and epistemic uncertainties are considered recently in the structural analysis and design optimization. The reliability based de-sign optimization (RBDO) method [1] is used when the amount of input data is sufficient enough to create accurate statistical distribution. On the other hand, when the sufficient input data are not available due to limitations in time, human, and facility resources, the optimum design may not be reliable if RBDO method is used. To deal with the situation that input uncertainties have insufficient information, a possibility (or fuzzy set) method can be used for structural analysis and possibility based design optimization (PBDO) [2]. However, in many industry design problems, we may have to deal with design problems that involve with the mixed input statistical random and fuzzy variables simultaneously. For these problems, RBDO may yield unreliable optimum designs because of insufficient data. On the other hand, treating the random variables as fuzzy variables and invoking PBDO to solve the mixed design variable problem may yield too conservative designs with higher optimum costs. This paper proposes a new mixed variable design optimization (MVDO) problem based on the performance measure approach (PMA) [1]. To evaluate the possibilistic constraint in MVDO, a sub-optimization problem for inverse analysis is carried out using a hyper-cylinder domain. To solve this sub-problem efficiently and effectively, a new numerical algorithm, maximum failure search (MFS) method, is proposed in this paper by combining the enhanced hybrid mean value (HMV+) method [3] for the inverse reliability analysis in RBDO and the maximal possibility search (MPS) method [2] for the inverse possibility analysis in PBDO. Some mathematical examples are used to demonstrate the efficiency and effectiveness of the proposed numerical MFS method. Some physical design examples are used to compare the proposed MVDO results with RBDO and PBDO results.

The usual approach in structural design optimization requires that at each iteration of the numerical optimization algorithm, a set of finite element analysis equations are solved to compute the objective/constraint functions. Such a nested solution procedure is straightforward because optimization and analysis processes are kept separate, but wasteful since a complete analysis is performed for each intermediate non-optimal design (one at each iteration). This paper illustrates an economical alternative approach where the finite element equations are formulated as part of the optimization problem by treating the unknowns as design variables and equations as equality constraints. This integrated problem can be solved using a spreadsheet application which serves as a highly suitable platform for integrating and solving the optimization and analysis simultaneously since all spreadsheet cells are interlinked. Together with widely available spreadsheet software, these techniques represent a very convenient tool not just for engineers to learn about the subject of design optimization, but also to gain physical insight into their design problems and perform design optimization routinely in their work.

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.

An efficient combination of multi-objective evolutionary optimization and reliability analysis for reliability-based design optimization of truss structures

We derive the isogeometric configuration sensitivity of the Mindlin plates by using the material derivative and adjoint approaches. This is utilized in the shape design optimization that includes a variation of design components in its shape and orientation. By the isogeometric approach, the NURBS basis function in CAD system is directly utilized in the response analysis, which enables the seamless incorporation of higher continuity and exact geometry such as curvature and normal vector into the computational framework. The impact of exact curvature in the bending problem of Mindlin plates on the configuration design sensitivity is demonstrated through numerical examples. The obtained design sensitivity is further utilized in the shape design optimization of built-up structures. Due to the non-interpolatory property of the NURBS basis functions, a mismatch of patches in the built-up structures could occur during the isogeometric design optimization, which can be easily resolved using transformed basis functions.