In topology optimization (TO) for additive manufacturing (AM), considering the anisotropy of formed materials induced by layer-by-layer AM processes is an emerging challenge. Based on this special process-related anisotropic constitutive relationship, a lightweight TO framework that considers both strength and stiffness requirements is proposed and explored in this work. Firstly, by introducing a print-off angle variable related to the anisotropy, the classical transversely isotropic model is extended to simulate the process-related anisotropic constitutive behavior. Then, based on the Hoffman failure criterion, a process-related anisotropic failure strength measurement is established. Furthermore, to achieve effective strength control, a global aggregation strategy based on the P-norm and error correction techniques is constructed. On this basis, the classical volume minimization is extended to include both anisotropic strength and stiffness constraints. Additionally, to address the convergence difficulties caused by the angle periodicity, an adaptive adjustment strategy for the angle variation is applied. The sensitivities related to the density and angle variables are derived in detail to adapt to gradient-based optimization algorithms. Typical numerical examples validate the effectiveness of the proposed method. The results reveal the inherent trade-off between lightweight, structural safety, and stiffness performance in the design. By effectively utilizing the process-induced anisotropy, the proposed algorithm reduces material usage while ensuring structural stiffness and strength requirements.

This work addresses a challenging problem in high-performance design for additive manufacturing (AM): considering AM process-induced material anisotropy in structural topology optimization with stiffness and strength requirements. A novel formulation for minimizing anisotropic failure strength with stiffness and material volume constraints is proposed, by integrating a newly constructed AM process-related anisotropic material model. Specifically, the building direction angle (as a key design variable) is introduced into the orthogonal anisotropy material model to quantify the AM process-induced anisotropic mechanical properties. A tailored anisotropic failure index is developed as the minimization objective to achieve high-performance design. And, a strength ratio-based Hoffman failure function is proposed to avoid the locally over-conservative design caused by the traditional non-homogeneous failure criterion. In addition, the P-norm-based global aggregation and error correction techniques are employed to obtain reasonable strength measurement. The adaptive reduction strategy for the feasible region of angle variables is applied to address the convergence difficulties caused by the periodicity of trigonometric functions related to angle variables. Moreover, the sensitivities related to density and angle variables are derived in detail. Typical numerical examples illustrate the proposed methods. Due to the rational utilization of the AM process-induced material anisotropy, the proposed algorithm significantly improves structural strength while ensuring structural stiffness, and the optimization process also becomes easy to converge.

This paper addresses key challenges in the topology optimization of multi-cracked structures, including crack removal, coupling effects, and the singular behavior of stress intensity factors (SIFs). A new optimization framework is developed by integrating the Solid Isotropic Material with Penalization (SIMP) method and the extended finite element method (XFEM). Within this framework, an adaptive penalty strategy for stress intensity factors (SIF-APS) is proposed. By employing the density field in the crack-tip region as a carrier, SIF-APS combines crack geometry and material distribution so that it adaptively penalizes SIFs at crack tips. This strategy effectively mitigates the numerical issues associated with element deactivation in conventional methods, which often lead to distorted fracture responses as well as singularities in SIFs. Furthermore, the proposed framework explicitly incorporates multi-crack coupling effects into the optimization model. This establishes a general and versatile approach for multi-cracked structures. Numerical validation through both benchmark problems and an engineering-inspired case confirmed the effectiveness of the method in complex crack scenarios. The results demonstrate that the proposed approach significantly enhances the resistance of structures against cracking while achieving lightweight design, and adaptively captures the coupling effects induced by variations in crack spacings, lengths, orientations, and positions.

This work aims to address the critical challenge of process-induced anisotropy in additive manufacturing (AM) by developing a topology optimization framework that simultaneously controls structural stiffness and anisotropic failure strength. The scope encompasses the integration of print-off angle-dependent material behavior into the design process, specifically targeting AM components exhibiting transversely isotropic properties due to layer-by-layer fabrication. The methodology introduces the print-off angle into an anisotropic constitutive model to characterize the mechanical response of AM components. The Hoffman failure criterion is extended to describe process-induced anisotropic strength. A concurrent optimization framework for structural topology and print-off angle is established using the classical density-based method. Numerical techniques, including the density filtering, threshold projection, P-norm global aggregation, error correction, and adaptive reduction strategy, are integrated to address numerical challenges. Sensitivities related to density and angle variables are derived in detail to enable an efficient solution based on the gradient-based optimization algorithms. Numerical examples demonstrate that the proposed method effectively reduces the risk of anisotropic failure compared to conventional isotropic design approaches. The results reveal that optimal print-off angles align material principal axes with principal stress trajectories, thereby improving the load-bearing efficiency of optimized structures. The optimized designs more objectively characterize the true mechanical behavior of AM components, providing a pathway toward safer and more reliable AM-dedicated structures.

Bi-modulus materials exhibiting distinct tensile and compressive moduli (e.g., concrete, fiber-reinforced composites, etc.) have been widely used in fields such as civil engineering and aerospace. However, due to the non-smoothness and strain state-dependency of the constitutive model and the design manufacturability, conventional linear elasticity-based topology optimization (TO) methods are difficult to apply to such problems. To this end, this work makes the first attempt to incorporate both bi-modulus material properties and self-supporting constraints into a unified TO framework for additive manufacturing. To overcome the above bi-modulus constitutive challenge, an improved smooth constitutive model retaining complete shear modulus information is established, and the exact tangent stiffness matrix for Newton–Raphson iterations is derived. To tackle the self-supporting design challenge, a density-gradient-based geometric self-supporting constraint is embedded into the bi-modulus TO framework and extended from 2D to 3D On this basis, a two-level solution strategy combining an outer TO loop with an inner nonlinear finite element analysis loop is established. Typical 2D and 3D numerical examples validate the effectiveness of the proposed method and reveal the influence of key parameters, such as the tension–compression modulus ratio and the overhang angle threshold, on the optimized designs.

The modeling of complex geometries with cutouts in NUBRS-based isogeometric analysis usually needs a multiple-patches strategy. It is still an obstacle because of the requirement of very specialized knowledge of computer-aided design (CAD) to generate a NURBS mesh. In this paper, a cut NURBS element method is proposed for the free vibration and buckling analysis of the complex-shaped laminate Reissner-Mindlin plate. Here, three major issues including the shearing locking, the representation of the cut objects, and the localized eigenmodes must be addressed. Firstly, in order to address these issues, an artificial shear correction factor is introduced to avoid shearing locking. Secondly, a level set approach on a structured NURBS mesh is used to produce the cut NURBS element as well as describe the arbitrary and crisp interface between the cut objects and the initial simple geometry through the thresholding of the level set value. Then, a segmented density method is adopted to represent the contribution of the solid, void, and cut NURBS elements. Finally, the different density interpolation formulas for element stiffness, mass, and geometrical matrices are introduced to overcome localized eigenmodes. The numerical results show the proposed method can effectively avoid the existence of shear locking and localized eigenmodes. By comparing with the results from other methods, the proposed method is proven to obtain highly accurate numerical results and effectively reduce computational cost.

Recent experiments have demonstrated that high-density space charge around a structure can shield precipitation-static on the structure’s surface, while high-velocity fluid can weaken this shielding effect. The physical mechanism behind this phenomenon remains unclear due to the limitations of experimental conditions and theoretical developments. To address this question, we propose a theoretical model to describe the process of precipitation-static, which captures multi-physics coupling effects including fluid field, particle motion and electric field. We also propose a method to describe the motion state of the charged particles in precipitation-static. We find that high-velocity fluid can weaken the shielding effect of space charge against precipitation-static by altering the forces exerted on charged particles, affecting their motion and spatial distribution as well as reducing the density of space charge around structure. Our findings emphasise the indispensability of considering fluid dynamics in understanding precipitation-static and offer valuable insights for future research.

Waveguide rod can be used for acoustic emission (AE) monitoring of broken wires in prestressed steel strands of bridges, however, the propagation and attenuation characteristics of AE waves in the waveguide rod lead to the need to arrange a larger number of sensors for structural monitoring to meet the monitoring requirements, which increases the economic cost of monitoring. For the reason, this paper proposes to embed acoustic black hole (ABH) in the traditional cylindrical waveguide rods to realize the enhancement of the damage signal of the AE source, which can increase the monitoring range of the structure, reduce the number of AE sensors used and the investment of monitoring costs. In this paper, the theory of AE wave propagation in ABH waveguide rod is established, and the geometric model of the ABH structure embedded in cylindrical waveguide rods is constructed. The propagation mechanism of the AE wave in the ABH waveguide rod is visualized by numerical simulation method, and the propagation models of the AE wave in the ABH structure are established. The optimal arrangement of AE sensors in the ABH position is determined by experimental studies, and the influence of the ABH geometric parameters on the enhancement efficiency of the AE wave signals of the damage source as well as waveforms is analyzed. The results show that the ABH waveguide structure can realize the AE signal enhancement, the AE wave will be reflected in a “counterclockwise” manner in the ABH with a truncation height, and the amplitude of the AE wave follows the power exponential function to increase when it propagates to the direction of the ABH truncation height. AE sensors are arranged in the end of the ABH to achieve the best signal enhancement effect, and the ABH length and power index are positively correlated with AE amplitude enhancement efficiency. The ABH waveguide rod has not produce significant changes to the main frequency range of the damage AE source. Therefore, the ABH waveguide rod method proposed in this paper can realize signal enhancement and provide a theoretical basis for the sensor arrangement method of acoustic emission technology (AET) in structural health monitoring.

Fiber-reinforced composites are an ideal material for the lightweight design of aerospace structures. Especially in recent years, with the rapid development of composite additive manufacturing technology, the design optimization of variable stiffness of fiber-reinforced composite laminates has attracted widespread attention from scholars and industry. In these aerospace composite structures, numerous cutout panels and shells serve as access points for maintaining electrical, fuel, and hydraulic systems. The traditional fiber-reinforced composite laminate subtractive drilling manufacturing inevitably faces the problems of interlayer delamination, fiber fracture, and burr of the laminate. Continuous fiber additive manufacturing technology offers the potential for integrated design optimization and manufacturing with high structural performance. Considering the integration of design and manufacturability in continuous fiber additive manufacturing, the paper proposes linear and nonlinear filtering strategies based on the Normal Distribution Fiber Optimization (NDFO) material interpolation scheme to overcome the challenge of discrete fiber optimization results, which are difficult to apply directly to continuous fiber additive manufacturing. With minimizing structural compliance as the objective function, the proposed approach provides a strategy to achieve continuity of discrete fiber paths in the variable stiffness design optimization of composite laminates with regular and irregular holes. In the variable stiffness design optimization model, the number of candidate fiber laying angles in the NDFO material interpolation scheme is considered as design variable. The sensitivity information of structural compliance with respect to the number of candidate fiber laying angles is obtained using the analytical sensitivity analysis method. Based on the proposed variable stiffness design optimization method for complex perforated composite laminates, the numerical examples consider the variable stiffness design optimization of typical non-perforated and perforated composite laminates with circular, square, and irregular holes, and systematically discuss the number of candidate discrete fiber laying angles, discrete fiber continuous filtering strategies, and filter radius on structural compliance, continuity, and manufacturability. The optimized discrete fiber angles of variable stiffness laminates are converted into continuous fiber laying paths using a streamlined process for continuous fiber additive manufacturing. Meanwhile, the optimized non-perforated and perforated MBB beams after discrete fiber continuous treatment, are manufactured using continuous fiber co-extrusion additive manufacturing technology to verify the effectiveness of the variable stiffness fiber optimization framework proposed in this paper.

Engineering structures are prone to microcracking due to the influence of manufacturing processes or environmental conditions, while accurately simulating crack behavior remains complex. Consequently, the topological optimization of cracked structures presents a significant challenge in structural design. This paper proposes a topology optimization method based on the brittle fracture criterion for mixed-mode cracks, aimed at optimizing cracked structures. An optimization model is established to minimize volume while satisfying constraints on strength, stiffness, and crack resistance. The extended finite element method (XFEM) is employed to achieve high-accuracy simulations of crack behavior. Moreover, the sensitivity expressions for the stress intensity factor across different fracture modes are derived, and an innovative solution to the lightweight design problem of structures exhibiting mixed-mode fracture modes under a given load is presented. A comparative study of the lightweight design under different working conditions, including the presence or absence of cracks, is carried out using four benchmark cases and an engineering structure example. The influence of crack parameters such as length, location, and size on the optimized topology is also investigated. The results of numerical examples demonstrate that this proposed method provides an effective framework for generating topological structures that meet diverse requirements for stiffness, strength, and crack resistance.

This work addresses a challenging problem in the high-performance design for additive manufacturing (AM): improving the structural performance (stiffness and strength) by comprehensively utilizing the material intrinsic anisotropy (local) and process-induced anisotropy (global). A novel AM-oriented structural topology optimization considering multi-source anisotropic failure strength from printing space and material locality is proposed. Specifically, an effective anisotropic constitutive model with spatially-locally varying is proposed to couple the material intrinsic anisotropy and process-induced anisotropy. A Hoffman criterion-based multi-source anisotropic material failure model is established. To overcome the difficulties of effective control and solution of large-scale failure factors under spatial and local coupling conditions, the P-norm-based global aggregation strategy and approximation error correction technology are extended. In addition, the stability of optimization iterations is significantly improved by adaptively adjusting the feasible region of angle variables. Also, the relatively complex sensitivities that couple density, local material direction angle, and global building direction angle variables are derived. Typical numerical examples demonstrate the effectiveness of the proposed method. Meaningful numerical properties of structural topology optimization considering multi-source anisotropic failure strength are explored in depth. The importance of considering intrinsic and process-induced anisotropy in design for AM is revealed.

Laminate composite panels with arbitrary cut-outs in a thermal environment may suffer buckling failure because of thermal stress. To address this issue, a manufacturing-oriented thermal-buckling optimization model is proposed for the design of curvilinear fiber paths. Furthermore, instead of using the traditional finite element method (FEM) with high computational costs, a cut nonuniform rational basis spline (NURBS) element method was developed for the thermal buckling analysis of laminate composite panels with arbitrary cut-outs. In this method, a level-set function, segmented density interpolation formulas, and an artificial shear correction factor were developed to describe arbitrary cut-outs, to overcome localized eigenmodes, and to avoid shear locking. Furthermore, a NURBS-based level-set method was proposed to illustrate the curvilinear fiber paths. The norm of the gradient vector of the NURBS-based level-set function was used to express the gap/overlap constraint. Subsequently, a thermal buckling optimization framework with compliance and manufacturing constraints was formulated. The effectiveness of the proposed optimization framework was verified numerically.

This work proposes a structural topology optimization method to consider material anisotropy induced by additive manufacturing processes. To quantify the relationship between manufacturing processes and mechanical properties of formed materials, the building direction angle is introduced into a transversely isotropic material model as a design variable. An anisotropic material model related to the building direction is thus established. A parallel optimization framework for structural topology and building direction is proposed by extending the classical compliance minimization formulation. And, to be applicable to gradient-based optimization algorithms, sensitivities related to density and angle variables are derived separately. Especially, to overcome the convergence difficulties caused by the periodic angle variables, an adaptive reduction strategy for the feasible region of angle variables is proposed. Typical numerical examples verify the rationality of the proposed method. The results show that the building direction related process-induced anisotropy significantly affects the optimized structural properties. The fluctuation of the trigonometric functions related to the angle variables would lead to obvious iteration oscillation in the optimization process, which makes the optimization difficult to converge. The proposed adaptive reduction strategy is proven effective in addressing this challenge. Besides, typical numerical properties of the co-optimization of structural topology and building direction are also revealed.

The isogeometric analysis of variable-stiffness structures with curvilinear fibers has gained considerable research attention. However, dealing with structures that have complex cutouts poses challenges for isogeometric analysis. Additionally, the thermal-elastic behavior of variable-stiffness structures must be carefully considered, as they often operate in thermal environments. This study introduces a novel trimmed non-uniform rational basis spline (NURBS) method to address these challenges and investigate the thermal buckling behavior of variable-stiffness plates. The method generates trimmed NURBS elements using a level-set function on the initial NURBS mesh to describe complex geometries. Segmented density interpolation formulas are proposed to capture the contributions of different NURBS elements and to prevent localized eigenmodes. An artificial shear correction factor is introduced to mitigate shear locking. Several numerical examples with various boundary conditions and fiber configurations, are presented to demonstrate the high accuracy and low computational costs of the proposed method.

This work proposes and investigates a new multi-field-multi-constraint coupled topology optimization problem, in which stress control, design castability, and geometry dimensional shrinkage issues that are of concern to practical engineering are simultaneously considered. In the optimization proposal considered, a pair of special twin designs are generated using a two-projected-field scheme, which maintains a consistent topological configuration and uniform dimensional shrinkage variations during the optimization process. The implicit correlation between these twin designs poses major challenges to their independent stress and castability control. To this end, an appropriate formulation is presented by reasonably integrating stress and casting constraints into the optimization proposal with dimensional shrinkage. And, special numerical techniques including stress penalization, aggregation approximation, approximation correction, and regional regularization are appropriately introduced to construct an effective solution strategy. Typical numerical examples are operated to demonstrate the validity of the proposed method and systematically evaluate its numerical properties. The results indicate that in the absence of necessary stress control measures, the obtained twin designs cannot avoid local high-stress concentration under uniform dimensional shrinkage. In contrast, the proposed method can effectively address this issue, but at the cost of the design stiffness under a given material volume limit. As a result, twin designs used for blueprint and model designs that simultaneously meet stress, castability, and uniform dimensional shrinkage requirements are now readily available.

With the development of additive manufacturing technology for fiber-reinforced composite materials, topology optimization of fiber-reinforced composite laminates involving multiple materials and variable stiffness is gaining increasing attention. This study proposes an effective methodology for a Multi-scale and Multi-material Composite Anisotropic Penalization (MMCAP) model to investigate multi-scale and multi-material design optimization of a fiber-reinforced variable stiffness (VS) composite structure to minimize structural compliance. In the concurrent MMCAP model, the macroscopic multi-material structural topology and microscopic discrete fiber laying angle selection are introduced as independent design variables and optimized simultaneously. The modified Solid Isotropic Material with Penalization (SIMP) and the Discrete Material Optimization (DMO) approaches are utilized at the macro- and micro-scales, respectively, to realize a clear macroscopic multi-material structural topology and microscopic specific discrete fiber laying angle selection. Multi-material fiber-reinforced plastic (FRP) materials, such as carbon fiber–reinforced plastic (CFRP) and glass fiber–reinforced plastic (GFRP), are considered two types of solid materials in terms of structural volume cost. Sensitivity analysis of the structural compliance concerning the variables of the two geometrical scales is performed using the analytical sensitivity analysis method. The DMO approach is utilized to couple two geometrical scales: macroscopic topology and microscopic material selection. The capabilities of the proposed MMCAP are demonstrated by concurrent multi-material and multi-scale design optimization of composite panels. The influence of the number of discrete fiber laying angles on the structural compliance and optimized topology configuration is also been discussed. Numerical studies showed that the proposed MMCAP scheme can effectively realize multi-material and multi-scale design optimization of fiber-reinforced composite structure with achieving a clear macroscopic multi-material structural topology and microscopic fiber laying angle. The proposed MMCAP scheme provides a new implementation strategy for lightweight, multi-material, and multi-scale design optimization of composite materials, considering the design and manufacturing collaboration through additive manufacturing technology.

Solidification shrinkage and surface finishing cause the inevitable dimensional shrinkage between the blueprint and model designs, thereby creating huge cost and precision chal-lenges to casting designs. This paper proposes an efficient structural topology optimiza-tion approach to simultaneously achieve the blueprint and model designs with uniform dimensional shrinkage in only one optimization setting. An appropriate two-projected-field scheme is established to simulate the blueprint and model designs by extending the density-based threshold projection approach. And, an effective quantitative framework is constructed to precisely predict the shrinkage rules. Besides, to ensure the castability of both the two projected designs, the Poisson equation-based constraint method is subtly integrated with the two-projected-field scheme. More importantly, to reduce the com-putational burden involving multiple designs and constraints, an efficient formulation is presented by reasonably considering the projected fields in the objective and constraint functions. Typical 2D and 3D numerical examples as well as one real-world example are provided to validate the effectiveness of the proposed strategies. The results show that the traditional one-projected-field scheme is difficult to yield the model design through the filtered field associated with the blueprint design. The proposed approach enables this and can help engineers achieve predictable dimensional shrinkage in an optimization way. (c) 2023 Elsevier Inc. All rights reserved.

The study of acoustic emission waves propagation mechanism and attenuation laws for damage of prestressed steel strands is the theoretical basis for acoustic emission health monitoring of prestressed steel strands such as stay cables, slings, suspenders, and concrete structures. Firstly, the propagation mechanism of acoustic emission waves in prestressed steel strands is studied using numerical simulation methods. Secondly, the amplitude and energy attenuation laws of acoustic emission waves caused by damage of prestressed steel strands are analyzed by experimental research, and the amplitude and energy attenuation models of the influence of prestress level are constructed. Finally, the constructed acoustic emission attenuation models are analyzed in combination with practical engineering. The results show that numerical simulation visualizes the propagation path of acoustic emission waves in prestressed steel strands; With the increase of prestress levels, the acoustic emission frequency distribution of prestressed steel strands damage ranges from 100 to 200 kHz, with a dominant frequency of 160 kHz, the acoustic emission amplitude and energy attenuation coefficients decrease, and the amplitude attenuation is slower than the energy attenuation; The acoustic emission amplitude attenuation of prestressed steel strands damage in prestressed hollow slab beams is 5 times faster than that of steel strands without surrounding media.

Fiber-reinforced polymer (FRP) composite frames are the ideal main support structure in civil and aerospace engineering applications because of their excellent material and structural properties for high stiffness ratio, high strength ratio, large span, and so forth. This paper investigated strong singularity optimum problems of FRP composite frames under fundamental frequency constraints. An area/moment of inertia-density strategy, the adapted polynomial material interpolation (APLMP) strategy, was adopted. The APLMP strategy changes the physical relationship of a tube's bending stiffness and cross-sectional area to relax the local vibration frequency constraint. The specific manufacturing constraints for laminated composite were considered in the mathematical model with fixed fiber winding angles and sequence according to certain guidelines to reduce the heavy calculation burden. The artificial densities of the APLMP strategy, which are a function of the areas of the composite frame, were defined as the size and topology optimization variables. Extensive large-scale two-dimensional and three-dimensional numerical examples demonstrated the validity of the APLMP interpolation strategy for topology design optimization of FRP frames. It was proved that the APLMP strategy can solve the challenge of the strongly singular optimum for structure topology design optimization of composite frames with frequency constraints.