Minimum Compliance Research Articles

Capesize time charter equivalent optimization based on speed and environmental regulations

PurposeThis paper aims to identify the interplay of standard Capesize optimal speeds for time charter equivalent (TCE) maximization in the Australia–China iron ore route and the optimal speeds as an operational tool for compliance with the International Maritime Organization (IMO) carbon intensity indicator (CII).Design/methodology/approachThe TCE at different speeds have been calculated for four standard Capesize specifications: (1) standard Capesize with ecoelectronic engine; (2) standard Capesize with non-eco engine (3) standard Capesize vessel with an eco-electronic engine fitted with scrubber and (4) standard Capesize with non-eco engine and no scrubber fitted.FindingsCalculations imply that in a highly inflationary bunker price context, the dollar per ton freight rates equilibrates at levels that may push optimal speeds below the speeds required for minimum CII compliance (C Rating) in the Australia–China trade. The highest deviation of optimal speeds from those required for minimum CII compliance is observed for non-eco standard Capesize vessels without scrubbers. Increased non-eco Capesize deployment would see optimal speeds structurally lower at levels that could offer CII ratings improvements.Originality/valueWhile most of the studies have covered the use of speed as a tool to improve efficiency and emissions in the maritime sector, few have been identified in the literature to have examined the interplay between the commercial and operational performance in the dry bulk sector stemming from the freight market equilibrium. The originality of this paper lies in examining the above relation and the resulting optimal speed selection in the Capesize sector against mandatory environmental targets.

An improved integrated framework based nodal density variable and Voronoi polygon for FE-based topology optimization

In this paper, an improved integrated framework is developed to deal with the numerical instability problems in FE-based topology optimization design methods. The proposed method mainly consists of two coupled computational layers: the upper layer for material geometric description, and the lower layer for structural analysis and sensitivity calculation. In the upper layer, the design domain is discretized by Delaunay triangulation, and a smooth and continuous material density description is obtained by interpolating the densities at nodes of Delaunay triangulation with Shepard interpolants. In the lower layer, the dual Voronoi polygon for Delaunay triangulation is used to generate the finite element mesh, and the virtual element method is applied to handle Voronoi polygon for structural response. Following this framework, the separate description of density distribution avoids the problem of geometric description relying on FE mesh in some existing work. Meanwhile, the use of Voronoi polygon provides more accurate finite element discretization of constantly changing material distributions. Typical numerical examples for the minimum compliance optimization problem reveal that the proposed method can eliminate checkerboards and mesh-dependencies effectively, and get approximate discrete 0/1 solutions without any filter. The simulation results demonstrate the efficiency and robustness of the proposed formulation and numerical techniques.

On the multi-objective perspective of discrete topology optimization in fluid-structure interaction problems

Fluid-structure interaction is a challenging topic that addresses fluid and solid physics, as well as the stress coupling between them. Traditional topology optimization methods are performed with coupling load interpolation schemes in order to have some information on fluid flow sensitivity analysis and improve compliance minimization into design-dependent problems. In this paper, we propose a strategy to design fluid-structure systems by combining solid and fluid objectives without the need for the coupling load interpolation scheme. Therefore, we investigate topology optimization applied to fluid-structure interaction problems via a multi-objective formulation. We combine structural compliance with some fluid flow objective functions (energy dissipation, downforce, and drag) subject to a volume constraint. We assume linear elasticity for the solid and the steady incompressible Navier-Stokes equations for the fluid. The optimization problem is solved by using sequential integer linear programming via the TOBS (Topology Optimization of Binary Structures) method with a geometry trimming (GT) technique. It is a gradient-based method that produces explicit (discrete) boundaries that are convenient for coupled physics problems. Numerical results are presented for two and three-dimensional problems considering low to moderate Reynolds numbers. We demonstrate that the proposed multi-objective approach yields physically meaningful designs with improved performance, highlighting that the incorporation of coupling load interpolation into fluid-structure interaction optimization is redundant.

Bayesian optimization-based topology optimization using moving morphable bars for flexible structure design problems

This paper presents a Bayesian optimization (BO) based topology optimization to solve flexible structure design problems in highly nonlinear design spaces. Our primary interest is to avoid topology optimization’s strong dependency on initial designs, which is inevitable when employing gradient-based optimizers. In order to do this, BO is used as a gradient-free optimizer that uses a probabilistic model to trade off exploration and exploitation in order to balance global and local search with a minimal number of iterations. Because of the curse of dimensionality in BO, a moving morphable bar (MMB) is used as a primitive member for a low-dimensional surrogate. We verified that BO could handle dozens of design parameters using the MMB through mean compliance minimization problems with known global optimum layouts. The effect of the BO trade-off parameter in the acquisition function, balancing the optimizer’s exploration, is also investigated. Numerical examples show that the proposed BO-based topology optimization method has suggested better optimum solutions for flexible structures than the MMA-based topology optimization. The performance of the proposed method is also compared with other global optimization methods, showing better performance in terms of minimized objective functions as well as the number of analyses for convergence.

Topology optimization of periodic structures for crash and static load cases using the evolutionary level set method

Assembly complexity and manufacturing costs of engineering structures can be significantly reduced by using periodic mechanical components, which are defined by combining multiple identical unit cells into a global topology. Additionally, the superior energy-absorbing properties of lattice-based periodic structures can potentially enhance the overall performance in crash-related applications. Recent research developments in periodic topology optimization (PTO) have shown its efficacy for tackling new design problems and finding advanced novel structures. However, most of these methods rely on gradient information in the optimization process, which poses difficulties for crash problems where analytical sensitivities are usually not directly applicable. In this paper, we present an effective periodic evolutionary level set method (P-EA-LSM) for the optimization of periodic structures. P-EA-LSM uses a low-dimensional level-set representation based on moving morphable components to parametrize a single unit cell, which is replicated in the design domain according to a predefined pattern. The unit cell is optimized using an evolutionary algorithm and the structural responses are calculated for the entire system. We initially assess the performance of P-EA-LSM using three 2D minimum compliance test cases with varying periodicities. Our results demonstrate that our approach produces solutions comparable to other state-of-the-art methods for PTO while keeping a low dimensionality of the optimization problem. Subsequently, we effectively evaluate the capabilities of P-EA-LSM in a crashworthiness scenario. This particular application highlights the significant potential of the method, which does not rely on analytical sensitivities.

Efficient multi-material topology optimization design with minimum compliance based on ResUNet involved generative adversarial network

Efficient multi-material topology optimization design with minimum compliance based on ResUNet involved generative adversarial network

HiTop 2.0: combining topology optimisation with multiple feature size controls and human preferences

ABSTRACT Topology optimisation is a computational design approach that generates high-performing, efficient structures uniquely suited to a design engineer’s goal. However, there exist two major obstacles to the accessibility, or ease of use, of topology optimisation: expensive computational costs and users’ binary decision between personal intuition and the algorithm’s result. Human-informed topology optimisation, or HiTop, presents an alternative approach to topology optimisation when a user lacks access to a high-performance computer or knowledge of code parameters. HiTop 2.0 prompts users to interactively identify a region of interest in the preliminary design and modify the size of the solid and/or void features. The novel contribution of this paper implements multi-phase minimum and maximum solid feature size controls in HiTop 2.0, and demonstrates 2D and 3D benchmark examples, including test cases that show how the user can interactively enhance issues related to eigenvalues, stress, and energy absorption, while solving the minimum compliance problem.

Topology optimization on metamaterial cells for replacement possibility in non-pneumatic tire and the capability of 3D-printing.

One of the applications of mechanical metamaterials is in car tires, as a non-pneumatic tire (NPT). Therefore, to find a suitable cell to replace the pneumatic part of the tire, three different solution methods were used, including topology optimization of the cubic unit cell, cylindrical unit cell, and fatigue testing cylindrical sample (FTCS). First, to find the mechanical properties, a tensile test was conducted for materials made of polylactic acid (PLA) and then, the optimization was done based on the weight and overhang control for the possibility of manufacturing with 3D printers, as constraints, besides, the objective of minimum compliance. In the optimization of the cubic unit cell, the sample with a minimum remaining weight of 35% was selected as the optimal sample. However, for the cylindrical unit cell, a sample with a weight limit of 20% was the most optimal state. In contrast, in the FTCS optimization, a specimen with lower remaining weight equal to 60% of the initial weight was selected. After obtaining the answer, five cells in the FTCS and two mentioned cells were evaluated under compressive testing. The samples were also subjected to bending fatigue loadings. The results demonstrated that cellular structures with 15% of lower weight than the optimized samples had the same fatigue lifetime. In the compressive test, the line slope of the specimens with cellular structures in the elastic region of the force-displacement diagram was reduced by 37%, compared to the completely solid samples. However, the weight of these samples decreased by 59%. Furthermore, the fracture surface was also investigated by field-emission scanning electron microscopy. It was observed that a weak connection between the layers was the cause of failure.

The Role of Extrinsic Motivation in Securing Actors’ Compliance with the International Anti-Money Laundering/Counterterrorist Financing Regime

Abstract The effectiveness of the Financial Action Task Force (FATF) international regime to govern anti-money laundering (AML) and counterterrorist financing (CTF) has been questioned since its establishment. In theory, the FATF’s network of multilevel actors should protect the integrity of the international financial system. The empirical evidence in this article shows that the FATF has made a difference in ensuring states’ (official) compliance with its measures, using extrinsic motivation tools; for example, ranking noncompliant states. However, it argues that such motivation only ensures actors’ minimum compliance, meaning that the regime’s effectiveness is suboptimal, while fostering intrinsic motivation would improve actors’ performance. Therefore, it is essential to understand why actors comply with the FATF approach and how they could be persuaded to achieve better compliance so that the regime’s effectiveness is feasible. This article explores these questions, using interviews with thirty practitioners in three locations, supported by a qualitative analysis of documentary data.

Concurrent topology optimization of shells with pattern-guided infills for intuitive design and additive manufacturing

This paper introduces a systematic design optimization approach for shells with pattern-guided infills, aiming to address both intuitive design requirements and considerations for additive manufacturing. The approach utilizes a density-based topology optimization method and assigns two sets of design variables to distinctly define the base, coating, and infill structures. By evolving the solid shells and enriched infills concurrently, the design optimization process ensures a cohesive integration of both components. To guide the infill design towards matching the geometrical features of a predefined pattern, a geometrical constraint is imposed on the infill field. Enhanced by an updated and approximate volume constraint, the infill materials with prescribed appearance performances are accordingly distributed in the base region. The simultaneous optimization of shell geometry and infill layout is then performed within the framework of minimum compliance topology optimization. A range of numerical results illustrate the effectiveness and robustness of the proposed approach. The topology optimized results demonstrate that a given pattern can directly control the design features of the infill in a visually explicit manner and the shell-infill composites ensure convenient manufacturability.

Bending behaviour of a topologically optimised ABS mesostructures 3D printed by the FDM process: numerical and experimental study

This paper is intended to investigate numerically and experimentally the influence of raster angle on the structural performance of an optimised printed structure.The topology optimisation (TO) problem for compliance minimisation using Solid Isotropic Material with Penalization (SIMP) method has been solved with a Messerschmitt-Bolkow-Blohm (MBB) beam under three-point bending, then the resulting optimal design was additively manufactured using Fused Filament Fabrication (FFF) with varying raster angle. The mechanical behaviour of these geometries was investigated and compared. A numerical approach has been developed through a script in Python based on the G-code file and integrated into an ABAQUS to create a virtual sample identical to the physical specimen. The numerical results were coupled with an experimental investigation.The investigation presented in this work showed that the choice of raster significantly affects on the mechanical performance of the printed optimised structures. Indeed, the optimised structure printed with a 90 raster angle has the highest performance in contrast to 45 and 0, while the optimised structure printed at a 45 raster angle has an average performance. The experimental test validated the numerical data with an error of approximately 1.09%. Our numerical results are in good conformity with the experimental outcomes.In this research, we studied the impact of three raster angles (90, 45 and 0) on the mechanical behaviour of a FFF optimised part. The subsequent study will focus on the other print parameters, including the other raster angles.The analysis presented in this paper can be used for manufacturing a FFF optimised structure.This paper evaluates the effect of raster angle in printed optimised structures using a novel numerical approach. The presented results will establish a reference that many researchers can gear to develop the fabrication of TO structures by incorporating printing parameters.

Compliance Prediction for Structural Topology Optimization on the Basis of Moment Invariants and a Generalized Regression Neural Network.

Topology optimization techniques are essential for manufacturing industries, such as designing fiber-reinforced polymer composites (FRPCs) and structures with outstanding strength-to-weight ratios and light weights. In the SIMP approach, artificial intelligence algorithms are commonly utilized to enhance traditional FEM-based compliance minimization procedures. Based on an effective generalized regression neural network (GRNN), a new deep learning algorithm of compliance prediction for structural topology optimization is proposed. The algorithm learns the structural information using a fourth-order moment invariant analysis of the structural topology obtained from FEA at different iterations of classical topology optimization. A cantilever and a simply supported beam problem are used as ground-truth datasets, and the moment invariants are used as independent variables for input features. By comparing it with the well-known convolutional neural network (CNN) and deep neural network (DNN) models, the proposed GRNN model achieves a high prediction accuracy (R2 > 0.97) and drastically shortens the training and prediction cost. Furthermore, the GRNN algorithm exhibits excellent generalization ability on the prediction performance of the optimized topology with rotations and varied material volume fractions. This algorithm is promising for the replacement of the FEA calculation in the SIMP method, and can be applied to real-time optimization for advanced FRPC structure design.

Topology Optimization: Applications of VFLSM and SESO in the Generation of Three-Dimensional Strut-and-Tie Models

Topology Optimization: Applications of VFLSM and SESO in the Generation of Three-Dimensional Strut-and-Tie Models

A hole-filling based approach to controlling structural complexity in topology optimization

Shape and topology optimization problems are usually associated with geometrical restrictions. Effective control of structural complexity during the optimization process is important for various considerations, e.g., functionality, manufacturability, and aesthetics. Most existing approaches characterize structural complexity as the number of cavities. However, for three-dimensional structures, the genus (i.e., the number of tunnels) should also be considered as an additional topological constraint. In this paper, a hole-filling method is integrated into the bi-directional evolutionary structural optimization (BESO) computational framework to control the number and size of existing cavities and tunnels during the form-finding process. In the hole-filling method, excess cavities are filled with solid material and excess tunnels are covered by building sheet-like patches. The minimum size of the truss-like components and the minimum thickness of the sheet-like components can be controlled separately. Several two- and three-dimensional compliance minimization problems are presented to demonstrate the effectiveness and potential applications of the proposed approach. The structural performances of the optimized structures with and without complexity control are compared and analyzed. The results show that the developed methodology can produce structurally efficient designs with controllable topologies. It is also demonstrated that the generation of sheet-like components can considerably increase the stiffness of the optimized structure. The proposed approach is capable of generating diverse and competitive designs for architects and engineers to achieve a fine balance between architectural novelty and structural efficiency.

The Impact of Additive Manufacturing Constraints and Design Objectives on Structural Topology Optimization

To analyze the impact of different objective functions and additive manufacturing (AM) constraints on structural topology optimization, it is necessary to perform an in-depth comparative study. This analysis should consider specific structural design factors, such as compliance, volume, or stress minimization, and assess their effects on the topology optimization for AM. In addition, the inclusion of AM constraints can have a significant influence on various aspects, including optimal part geometry, part volume, support structure volume, and structural performance. Thus, it is essential to investigate and compare these factors to determine the optimal part design for AM. This study focuses on comparing topology optimization results obtained using compliance, stress, or multi-objective minimization, with and without AM constraints. A comparative analysis was conducted in the study, utilizing three structural design examples: cantilever beam, bridge-shaped structure, and L-shaped beam. The comparison results provide insights into the effects of build orientation, AM constraints such as overhang, and different design objectives on the structural topology optimization for AM.

A complete Physics-Informed Neural Network-based framework for structural topology optimization

Physics-Informed Neural Networks (PINNs) have recently gained increasing attention in the field of topology optimization. The fusion of deep learning and topology optimization has emerged as a prominent area of insightful research, where minimization of the loss function in neural networks can be comparable to minimization of the objective function in topology optimization. Inspired by concepts of PINNs, this paper proposes a novel framework, ‘Complete Physics-Informed Neural Network-based Topology Optimization (CPINNTO)’, to address various challenges in topology optimization, particularly related to structural optimization. The key innovation of the proposed framework lies in introducing the first complete machine-learning-based topology optimization framework through integration of two distinct PINNs. Herein, the Deep Energy Method (DEM) PINN is implemented to determine the deformation state of corresponding structures numerically. In addition, derivation of the objective function with respect to design variables is replaced with automatic differentiation in sensitivity-analysis PINN (S-PINN). The feasibility and potential of the CPINNTO framework have been assessed through several case studies while highlighting strengths and limitations of utilizing PINNs in topology optimization. Subsequent findings indicate that CPINNTO can achieve optimal topologies without labeled data nor FEA. The numerical examples demonstrate that CPINNTO is capable of stably obtaining optimal structures for various topology optimization applications, including compliance minimization problems, multi-constrained problems, and three-dimensional problems. Resulting designs exhibit favorable compliance values comparable to the designs obtained via density-based topology optimization. In summary, the proposed CPINNTO framework opens up novel and interesting possibilities for structural topology optimization.

A multigrid assisted reanalysis method for accelerated heat transfer topology optimization

Heat sinks are widely applied in industry, and heat transfer topology optimization can improve their performance while saving materials. However, the prohibitive computational cost hinders its development. Therefore, the Multigrid Assisted Reanalysis (MGAR) method is proposed to address the issue. The Combined Approximate Reduced Order Model (CAROM) is employed to reduce the dimensionality of governing equations, and computational efficiency is significantly improved. In addition, CAROM should be dynamically updated to ensure the accuracy of solutions, thus constructing the CAROM also take up a major computational cost. For this purpose, the V-cycle multigrid is employed to construct basis vectors of CAROM instead of direct solvers. Since the MGAR involves almost no matrix decomposition, except for solving the reduced linear systems, the MGAR is equipped to handle large-scale problems due to the advantage of high computational efficiency and low memory requirements. The competence of the MGAR is verified by several cases including thermal compliance minimization and maximum temperature minimization.

A topology-based in-plane filtering technique for the combined topology and discrete fiber orientation optimization

This work proposes a filtering technique for the concurrent and sequential finite element-based topology and discrete fiber orientation optimization of composite structures. The proposed filter is designed to couple the morphology with the topology of the structural domain throughout the optimization process in a way such that it suppresses the impact of the close-to-void finite elements’ morphology on the overall morphology of the structure while steering at the same time the local fiber orientation towards the neighboring topologically dense areas of the geometry. The functionality of the filter becomes crucial at the boundaries of the optimized structure, where the fiber orientation is forced to conform to the morphology of the local boundaries. The developed filtering technique is incorporated into both the concurrent and sequential finite element-based topology and discrete fiber orientation optimization problem, and the respective optimization problems are formulated for the compliance minimization of the composite structure. To assess the efficacy of the filter, it is demonstrated in the benchmark academic case studies of the 2D Messerschmitt-Bölkow-Blohm and cantilever beams when different state-of-art interpolation techniques are employed for modeling the discrete fiber orientation optimization problem.

An enhanced proportional topology optimization with virtual elements: Formulation and numerical implementation

This paper presents an improved non-sensitivity structural topology optimization method incorporating virtual elements with unstructured polygonal meshes. Specifically, we employ the recently developed gradient-free proportional topology optimization (PTO) approach, for the first time, together with a new material distribution formula suitable for both minimum compliance and compliant mechanism problems. In order to improve performance, we integrate a linear virtual element method (VEM) module into the PTO algorithm. The linear VEM has a desirable characteristic: it does not require numerical integration and, more importantly, is less sensitive to small-edge elements, thus, significantly reducing computational time. Additionally, we utilize virtual elements with unstructured polygonal meshes inside PTO to suppress one-node connection instabilities. Furthermore, the Heaviside-type operator in the main PTO algorithm loop enhances the optimized results by encouraging the density variables to approach discrete (0/1) solutions more effectively. We demonstrate the performance of our developed method in terms of computational speed, diversity of applications, and improved black-and-white (0/1) structures through several benchmark examples of compliance and compliant mechanism designs.

Quasi-Newton methods for topology optimization using a level-set method

The ability to efficiently solve topology optimization problems is of great importance for many practical applications. Hence, there is a demand for efficient solution algorithms. In this paper, we propose novel quasi-Newton methods for solving PDE-constrained topology optimization problems. Our approach is based on and extends the popular solution algorithm of Amstutz and Andrä (J Comput Phys 216: 573–588, 2006). To do so, we introduce a new perspective on the commonly used evolution equation for the level-set method, which allows us to derive our quasi-Newton methods for topology optimization. We investigate the performance of the proposed methods numerically for the following examples: Inverse topology optimization problems constrained by linear and semilinear elliptic Poisson problems, compliance minimization in linear elasticity, and the optimization of fluids in Navier–Stokes flow, where we compare them to current state-of-the-art methods. Our results show that the proposed solution algorithms significantly outperform the other considered methods: They require substantially less iterations to find a optimizer while demanding only slightly more resources per iteration. This shows that our proposed methods are highly attractive solution methods in the field of topology optimization.