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As a typical form of material imperfection, cracks generally cannot be avoided and are critical for load bearing capability and integrity of engineering structures. This paper presents a topology optimization method for generating structural layouts that are insensitive/sensitive as required to initial cracks at specified locations. Based on the linear elastic fracture mechanics model (LEFM), the stress intensity of initial cracks in the structure is analyzed by using singularity finite elements positioned at the crack tip to describe the near-tip stress field. In the topology optimization formulation, the J integral, as a criterion for predicting crack opening under certain loading and boundary conditions, is introduced into the objective function to be minimized or maximized. In this context, the adjoint variable sensitivity analysis scheme is derived, which enables the optimization problem to be solved with a gradient-based algorithm. Numerical examples are given to demonstrate effectiveness of the proposed method on generating structures with desired overall stiffness and fracture strength property. This method provides an applicable framework incorporating linear fracture mechanics criteria into topology optimization for conceptual design of crack insensitive or easily detachable structures for particular applications. [ABSTRACT FROM AUTHOR]

It is impractical to implement arbitrary-shaped piezoelectric patches from the view point of manufacturability of fragile piezoelectric ceramics, thus using designable electrode layers to deliver desired actuation forces provides a more realistic option in engineering applications. This study develops a topological design method of surface electrode distribution over piezoelectric sensors/actuators attached to a thin-walled shell structure for reducing the sound radiation in an unbounded acoustic domain. In the optimization model, the sound pressure norm at specific reference points under excitations at a certain excitation frequency or in a given frequency range is taken as the objective function. The pseudo densities for indicating absence and presence of surface electrodes at each element are taken as the design variables, and a penalized relationship between the densities and the active damping effect is employed. The vibrating structure is discretized with finite element model for the frequency response analysis and the sound radiation analysis in the unbounded acoustic domain is treated by boundary element method. The applied voltage on each actuator is determined by the constant gain velocity feedback (CGVF) control law. The technique of the complex mode superposition in the state space, in conjunction with a model reduction transformation, is adopted in the response analysis of the system characterized by a non-proportional active damping property. In this context, the adjoint-variable sensitivity analysis scheme is derived. The effectiveness and efficiency of the proposed method are demonstrated by numerical examples, and several key factors on the optimal designs are also discussed. [ABSTRACT FROM AUTHOR]

Based on the element-free Galerkin (EFG) method, an analysis-independent density variable approach is proposed for topology optimization of geometrically nonlinear structures. This method eliminates the mesh distortion problem often encountered in the finite element analysis of large deformations. The topology optimization problem is formulated on the basis of point-wise description of the material density field. This density field is constructed by a physical meaning-preserving interpolation with the density values of the design variable points, which can be freely positioned independently of the field points used in the displacement analysis. An energy criterion of convergence is used to resolve the well-known convergence difficulty, which would be usually encountered in low density regions, where displacements oscillate severely during the optimization process. Numerical examples are given to demonstrate the effectiveness of the developed approach. It is shown that relatively clear optimal solutions can be achieved, without exhibiting numerical instabilities like the so-called 'layering' or 'islanding' phenomena even in large deformation cases. This study not only confirms the potential of the EFG method in topology optimization involving large deformations, but also provides a novel topology optimization framework based on element-free discretization of displacement and density fields, which can also easily incorporate other meshless analysis methods for specific purposes. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents an adaptive density point refinement approach for continuum topology optimization on the basis of an analysis-mesh separated material density field description based on nodal design variables. The Shepard interpolants are used to construct a strictly range-restricted density field over the design domain with the density design variables defined on a density point grid. Since the density points are defined independent of the finite element mesh, it is easy to refine the density point grid without remeshing the finite element model. A refinement criterion is given to identify the gray transitional regions to be adaptively refined in the subsequent optimization iterations. With such a refinement scheme, the topology optimization can start from a relatively coarse density point grid but still yields a desired higher resolution of the structural boundaries in the final design. Because refinements are only performed when and where necessary, this method is able to improve the boundary description quality of the optimal result with much less design variables as compared with the case of global refinement, and therefore can greatly reduce the computational burden involved in the sensitivity analysis and optimization process. Moreover, the percentage of transitional regions in the final solutions can also be reduced. Compared with using a uniformly globally-dense density point arrangement, this approach can achieve similar optimal designs but with much less computational cost. Numerical examples are given to demonstrate the effectiveness and efficiency of the present approach. [Copyright &y& Elsevier]

The sensitivity analysis of rigid viscoplastic deformation processes with application to metal preform design optimization is investigated. For viscoplastic constitutive models, the deformation process is path-dependent in nature and thus the sensitivity analysis of the deformation history is formulated in an incremental procedure. To this end, an algorithm is derived on the basis of the time integration scheme used in the primary finite element analysis, where the contact conditions are treated with the penalty method. The discretized equilibrium equations, as well as the time integration equations, are directly differentiated with respect to the design variables. The discrete form of the sensitivity equations is then solved with procedures similar to those used in the direct analysis, where the secant matrix decomposed in the direct analysis can also be utilized at each time instant. Thus the sensitivity of the deformation history is evaluated in a step-wise procedure. The present algorithm can be employed for the optimization of metal forming processes. The accuracy of the proposed sensitivity analysis as well as its applicability are demonstrated by numerical examples with reference to preform design optimization problems, where the aggregate function method is employed for converting the non-smooth Min–max type objective function into a numerically tractable one. [ABSTRACT FROM AUTHOR]

Abstract: Various methods have been developed to fabricate highly stretchable electronics. Recent studies show that over 100% two dimensional stretchability can be achieved by mesh structure of brittle functioning devices interconnected with serpentine bridges. Kim et al show that pressing down an inflated elastomeric thin film during transfer printing introduces two dimensional prestrain, and therefore further improves the system stretchability. This paper gives a theoretical study of this process, through both analytical and numerical approaches. Simple analytical solutions are obtained for meridional and circumferential strains in the thin film, as well as the maximum strain in device islands, which all agree reasonably well with finite element analysis. [ABSTRACT FROM AUTHOR]

Abstract: Intramolecular junctions (IMJs) formed by connecting two arbitrary carbon nanotubes (CNTs) can act as functional building blocks in circuits and components of CNT-based electronics devices. While extensive studies have been conducted on the atomic structural as well as electrical properties of IMJs and great advances have been achieved, mechanical response of IMJs under large deformation, which may exert significant effects on their electrical properties, are still not fully explored. In this paper, both molecular dynamics (MD) simulation and finite element (FE) analysis are employed to investigate the buckling behavior of IMJs under axial compression. The strain rate effects are firstly studied in the MD simulations. It is found that the critical compressive strain is not sensitive to the strain rate of relatively low range, but it exhibits a strong dependency upon the strain rate under high speed compression. In particular, a different failure mode may occur under ultra-high loading velocities. Based on the discussion on the strain rate effects, a reasonable loading velocity is suggested to be adopted in the subsequent MD simulations. In this study, the results of both the MD simulations and the FE analyses indicate that the critical compressive strain is dependent upon the length, radial dimensions of the IMJ but insensitive to the chirality of the IMJ. The comparison between the results of the MD simulations and the FE analyses also confirms that the FE analysis is able to provide useful insights into the compressive behavior of CNT-based IMJs with a much less computational cost. [ABSTRACT FROM AUTHOR]

Abstract: This paper investigates the optimal spatial distribution of single-channel actuation voltage in static structural shape control problem. It is pointed out that single-channel actuation voltage input for shape control applications is of practical importance due to its ease of implementation. The Mindlin plate theory is used in the finite element modeling of laminates with piezoelectric layers. The optimal distribution of the single-channel actuation voltage is formulated as a discrete optimization problem with tri-level design variables, where a least-square function measuring the structural shape error is to be minimized under a constraint on the control effort. Such a problem is then transformed into a continuous one by introducing element-wise artificial design variables defining the topological feature of the control voltage distribution. A power-law function relating the design variables and the applied voltages is proposed to penalize intermediate values of the design variables. Based on the sensitivity analysis, the problem is solved effectively using the MMA algorithm tailored for constrained least-square problems. Numerical examples presented demonstrate the validity of the proposed problem formulation and numerical approaches. [Copyright &y& Elsevier]

Abstract: The study addresses the perturbation-based stochastic finite element analysis and the robust design optimization of deformation processes of inelastic solids. The perturbation equations for the stochastic moment analysis of both steady-state and non-stationary processes are presented. An iteration scheme based on the secant system operator is given for the solution of the perturbation equations in case that a tangent matrix is not available. The robust design of deformation processes is stated as a two-criteria optimal design problem that attempts best mean properties of the outcome at minimum variability. The task is solved using optimization techniques based on sequential quadratic programming in conjunction with the stochastic finite element analysis. The proposed method is applied to the design of an extrusion die for robustness with respect to friction variability, and to a workpiece preform design problem. The numerical results show the potential of the method for applications regarding the design of robust deformation processes. [Copyright &y& Elsevier]

Abstract: The robust design of non-linear structures with path-dependent response is stated as a two-criteria optimization problem and is solved by the method of mathematical programming. To this end, the perturbation technique is applied in conjunction with the incremental loading procedure for the response moment analysis of path-dependent non-linear structural systems with random parameters. Furthermore, the sensitivities of mean and variance of the structural performance function are evaluated using direct differentiation in the framework of perturbation based stochastic finite element analysis. By introducing a weighting factor in the compound objective––resp. desirability function, and feasibility indices in the constraints, the mathematical model of structural robust design problem is formulated and is solved with a gradient-based algorithm. Numerical examples demonstrate the applicability of the presented method. [Copyright &y& Elsevier]

The robust design of structures with stochastic parameters is studied using optimization techniques. The first two statistical moments of the stochastic parameters including design variables are considered in conjunction with the second-order perturbation method for the approximation of mean value and variance of the structural response. In this framework, the sensitivities of the mean values and variances of the structural performance function with respect to the design variables are calculated for use in the optimization task. The robust design of structures is formulated as a multi-criteria optimization problem, in which both the expected value and the standard deviation of the objective function are to be minimized. The robustness of the feasibility is also taken into account by involving the variability of the structural response in the constraints. The two-criteria optimization problem is converted into a scalar one and is then solved by a gradient based optimization algorithm. To demonstrate the applicability of the presented method, numerical examples are given, involving static and dynamic response. [Copyright &y& Elsevier]

In most of the existing topology optimization studies of multi-material structures, the interface of different materials was assumed to be perfectly bonded. Optimal design based on the perfect-interface assumption may introduce the risk of failure caused by interface debonding. This paper presents an efficient multi-material topology optimization strategy for seeking the optimal layout of structures considering the cohesive constitutive relationship of the interface. Based on the color level set method to describe the topology and the interface, the interface behavior is simulated by combining the extended finite element method (XFEM) and the cohesive model on fixed mesh. This enables modeling of possible separation of material interfaces, and thus provides a more realistic model of multi-material structures. Furthermore, this interface modeling technique avoids the difficulty of re-meshing when tracking the moving cohesive interface positions during the optimization process. In the topology optimization model, the normal velocities defined on the level set points are considered as design variables. In conjunction with the adjoint-variable sensitivity analysis, these design variables are updated by using the mathematical programming approach and then used to interpolate the boundary velocities. These boundary velocities are extrapolated to the whole domain with the fast marching method and used to advance the structural boundary through the Hamilton–Jacobi equation. This topology optimization technique can handle multiple constraints easily in the framework of level set method and at the same time preserve the signed distance property of the level set functions. Two numerical examples are given to demonstrate the effectiveness of the present method. It is also revealed that the optimal design considering interface behavior may exhibit tension/compression non-symmetric topology, in which material interfaces mainly undergo compression. [ABSTRACT FROM AUTHOR]

Abstract: The steel–concrete composite beam bonded by adhesive has particular advantages over the traditional composite beam. Based on the experimental push-out test, this paper proposes a three-dimensional nonlinear finite element model for the mechanical behaviour simulation of bonded steel–concrete composite beams. The proposed numerical model is validated through comparisons between numerical results and experimental data. The effects of certain parameters, including the elastic modulus of adhesive, the adhesive layer’s thickness, the concrete strength, the bonding strength and the bonding area, are investigated. Numerical results show that the influence of most investigated parameters on the response of the bonded composites is very notable, while that of the adhesive layer’s thickness (variation within 3–15mm) is relatively small. [Copyright &y& Elsevier]

Abstract: It is meaningful to account for various uncertainties in the optimization design of the adhesive bonded steel–concrete composite beam. Based on the definition of the mixed reliability index for structural safety evaluation with probabilistic and non-probabilistic uncertainties, the reliability-based optimization incorporating such mixed reliability constraints are mathematically formulated as a nested problem. The performance measure approach is employed to improve the convergence and the stability in solving the inner-loop. Moreover, the double-loop optimization problem is transformed into a series of approximate deterministic problems by incorporating the sequential approximate programming and the iteration scheme, which greatly reduces the burdensome computation workloads in seeking the optimal design. The validity of the proposed formulation as well as the efficiency of the presented numerical techniques is demonstrated by a mathematical example. Finally, reliability-based optimization designs of a single span adhesive bonded steel–concrete composite beam with different loading cases are achieved through integrating the present systematic method, the finite element analysis and the optimization package. [Copyright &y& Elsevier]

For multi-material structures, ensuring material interface strength is particularly vital for their integrity and durability. In the present study, we incorporate material interfacial stress constraints into topology optimization of bi-material structures. A multi-material level set method, in conjunction with interface-conforming finite element meshes, is employed to describe the distribution of different material phases and to capture the evolution of the material interfaces. The use of interface-conforming meshes enables accurate analysis of both interfacial stresses and their design sensitivities. Noting that the interfacial strength failure is usually characterized by a tension/compression asymmetric mechanism, we adopt an equivalent interfacial stress (which was originally proposed for strength criterion concerning composite delamination) expressed by the interface tensile and tangential stresses in the considered strength criterion. To handle the local nature of such interfacial stress constraints, we propose a global stress measure, which is an approximation of the p-norm of the equivalent interfacial stress field. An adjoint sensitivity analysis scheme is derived by taking into account the interface transmission conditions. To treat multiple constraints (the volume constraints and the interfacial stress constraint) in level set-based topology optimization, the velocity field-level set method is employed. Numerical examples are presented to show effectiveness of the present method. It is also shown that the tension/compression asymmetric interfacial strength criteria may lead to asymmetric designs. • A TO method to constrain interfacial stresses in multi-material structures is proposed. • A globalized tension/compression asymmetric interfacial strength criterion is adopted. • Body-fitted mesh is used to provide accurate interfacial stress results. • Interface transmission conditions are considered in the sensitivity analysis. • The velocity-field level set method is employed to handle multiple TO constraints. [ABSTRACT FROM AUTHOR]

Membrane fixtures provide external tensile forces and boundary conditions for thin membranes; thus, they play an important role in the minor principal stress distribution and wrinkling patterns. Here, we propose a global optimization approach for designing the shape of membrane fixtures to suppress stress-related wrinkles under large membrane deformations. The objective of the optimization model is to maximize the minimal value of the in-plane minor principal stress over the entire membrane. This model incorporates the Kriging surrogate method, which is a robust optimization technique, to make the membrane in a taut state and to find out the global optimal solution. Several examples with different stretching displacements are presented to demonstrate the effectiveness of this proposed optimization method. Moreover, the method provides an efficient way to obtain wrinkle-free membrane structures without reducing the membrane area. [ABSTRACT FROM AUTHOR]

The stretch-induced wrinkling behaviors in graphene membranes with frozen zone are investigated in molecular dynamics simulations and suppressed by adopting optimal designs obtained in topology optimization. The graphene membranes with optimal designs under stretching are wrinkle-free, this is meaningful to ensure the exceptional performances of graphene-nanoelectronics. Both the wrinkling and wrinkling-suppression mechanisms are qualitatively and quantitatively elucidated with finite element analyses, which are helpful to understand the stretch-induced wrinkling in graphene membranes with frozen zone and to provide useful guidance to the design of the large-area graphene-nanoelectronics. [ABSTRACT FROM AUTHOR]

[Display omitted] • A system inverse design framework based on optimized bistable cells for constructing programmable multistable mechanical metamaterials is proposed. • Customized bistable cells with precise control of maximum instability force were designed using sensitivity-free topology optimization method. • According to the proposed design strategy, a programmable mechanical metamaterial with various target functionalities and deformation models has been developed. • Finite element analysis and experiments were used to demonstrate the specific complex deformations of the metamaterial. This study proposes a systematic inverse design framework for constructing multistable mechanical metamaterials with programmable gradients. Herein, we designed the tailored bistable cells with precisely controlled maximum instability forces through the topology optimization approach. Then, the designed bistable structures were programmed to construct the multistable mechanical metamaterials with different target gradient snapping sequences and deformation models. Consequently, the simulation and experimental results showed the feasibility of the design method, which successfully produced two- and three-dimensional mechanical metamaterial structures with different functions. Finally, we verified the expected deformation sequences and multistable behaviors of mechanical metamaterials by testing the designed specimens prepared via additive manufacturing. Overall, our findings show that the proposed design strategy offers a new paradigm for developing precisely tailored and programmable mechanical metamaterials. [ABSTRACT FROM AUTHOR]

Based on the first-order shear deformation (FOSD) hypothesis, a geometrically nonlinear finite element formulation is developed for static and dynamic analysis of carbon nanotube reinforced magneto-electro-elastic (CNT-MEE) plates. The nonlinear finite element model takes the fully geometrically nonlinear strain–displacement relations with large rotations. The nonlinear dynamic governing equations are derived using Hamilton's principle. The electric and magnetic potentials are assumed to be varied only along the thickness direction of CNT-MEE plates. Four functionally graded (FG) pattens, FG-U, FG-X, FG-O and FG-V are computationally studied for understanding the reinforcement efficiency of the magneto-electro-elastic matrix. The proposed geometrically nonlinear model is verified by comparing with the computational results from the literature. Furthermore, the volume fractions of CNT reinforcement material, distribution forms, reinforcement angles and volume fractions of MEE matrix material are studied by systematically in the computational simulation. These results can be used as a benchmark for designing and analyzing the magneto-electro-elastic properties of CNT-MEE structures with functionally graded reinforcements in extreme environments. [ABSTRACT FROM AUTHOR]

• Thickness variation promises diverse design of stretchable electronics. • Non-uniform theoretical models are developed for both global buckling and local folding. • The deformed configurations and maximum strains for buckled/folded film are predicted. • Concise analytical solutions help quick strain estimation and conceptual design of stretchable electronics. Thin film can either buckle globally or fold locally to assemble stretchable electronics, the variation of thickness in thin film leads to tunable structures and promises the diverse design of stretchable electronics. In this paper, theoretical models are developed to investigate the global-buckling and local-folding in the non-uniform thin film of stretchable electronics. The models are capable of giving concise and explicit analytical solutions of the deformed configuration and maximum strain in thin film. The effectiveness and accuracy of analytical solutions are verified by the finite element analyses (FEA) and molecular dynamics (MD) simulations. Our study provides useful guidance for the diverse design and precise control of stretchable electronics. Image, graphical abstract [ABSTRACT FROM AUTHOR]