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Three-dimensional printing technology using fused deposition modeling processes is becoming more and more widespread thanks to the improvements in the mechanical properties of materials with the addition of short fibers into the polymeric filaments. The final mechanical properties of the printed components depend, not only on the properties of the filament, but also on several printing parameters. The main purpose of this study was the development of a tool for designers to predict the real mechanical properties of printed components by performing finite element analyses. Two different materials (nylon reinforced with glass or carbon fibers) were investigated. The experimental identification of the elastic material model parameters was performed by testing printed fully filled dog bone specimens in two different directions. The obtained parameters were used in numerical analyses to predict the mechanical response of simple structures. Blocks of 20 mm × 20 mm × 160 mm were printed in four different percentages of a triangular infill pattern. Experimental and numerical four-point bending tests were performed, and the results were compared in terms of load versus curvature. The analysis of the results demonstrated that the purely elastic transversely isotropic material model is adequate for predicting behavior, at least before nonlinearities occur.

Non-linear fluid viscous dampers have found widespread applications in engineering practice for seismic mitigation of civil structures. Topology optimization has emerged as an appealing means to achieve the optimal design of non-linear viscous dampers in terms of both layouts and parameters. However, the conventional methodologies are mainly restricted to deterministic dynamic excitations. This research is devoted to the topology optimization of non-linear viscous dampers for energy-dissipating structures with consideration of non-stationary random seismic excitation. On the basis of the equivalent linearization—explicit time-domain method (EL-ETDM), which has been recently proposed for non-stationary stochastic response analysis of non-linear systems, an adjoint variable method-based (AVM-based) EL-ETDM is further proposed for non-stationary stochastic sensitivity analysis of energy-dissipating structures with non-linear viscous dampers. The stochastic response and sensitivity results obtained by EL-ETDM with high efficiency are utilized for topology optimization of non-linear viscous dampers with the gradient-based method of moving asymptotes. The optimization problem is formulated as the minimization of the maximum standard deviation of a critical response subjected to a specified maximum number of viscous dampers, and the p -norm function is employed for approximation of the non-smooth objective function. The existence information of each potential viscous damper as well as the damper parameters are characterized by continuous design variables, and the solid isotropic material with penalization technique is utilized to achieve clear existences of viscous dampers. Two numerical examples are presented to illustrate the feasibility of the proposed topology optimization framework.

We propose a topology optimization method for design of transversely isotropic elastic continua subject to high-cycle fatigue. The method is applicable to design of additive manufactured components, where transverse isotropy is often manifested in the form of a lower Young’s modulus but a higher fatigue strength in the build direction. The fatigue constraint is based on a continuous-time model in the form of ordinary differential equations governing the time evolution of fatigue damage at each point in the design domain. Such evolution occurs when the stress state lies outside a so-called endurance surface that moves in stress space depending on the current stress and a back-stress tensor. Pointwise bounds on the fatigue damage are approximated using a smooth aggregation function, and the fatigue sensitivities are determined by the adjoint method. Several problems where the objective is to minimize mass are solved numerically. The problems involve non-periodic proportional and non-proportional load histories. Two alloy steels, AISI-SAE 4340 and 34CrMo6, are treated and the respective as well as the combined impact of transversely isotropic elastic and fatigue properties on the design are compared.

This paper develops a non-probabilistic reliability-based topology optimization (NRBTO) framework for continuum structures under multi-dimensional convex uncertainties. Combined with the solid isotropic material with penalization (SIMP) model and the set-theoretical convex method, the uncertainty quantification (UQ) analysis is firstly conducted to obtain mathematical approximations and boundary laws of considered displacement responses. By normalization treatment of the limit-state function, a new quantified measure of the non-probabilistic reliability is then defined and further deduced by the principle of the hyper-volume ratio. For circumventing optimization difficulties arising from large-scale design variables, the adjoint vector scheme for sensitivity analysis of the reliability index with respect to design variables are discussed as well. Numerical applications eventually illustrate the applicability and the validity of the present problem statement as well as the proposed numerical techniques.

Purpose This study aims to analyse the behaviour of plane waves within a nonlocal transversely isotropic visco-thermoelastic medium having variable thermal conductivity. Design/methodology/approach The concept of enunciation is used in the generalized theory of thermoelasticity in accordance with the Green–Lindsay and Eringen’s nonlocal elasticity models. The linear viscoelasticity model developed by Kelvin–Voigt is used to characterize the viscoelastic properties of transversely isotropic materials. Findings It has been noticed that three plane waves, which are coupled together, travel through the medium at three different speeds. The derivation of reflection coefficients and energy ratios for reflected waves is carried out by incorporating suitable boundary conditions. Numerical computations are performed for the amplitude ratios, phase speeds and energy partition and displayed in graphical form. Originality/value The outcomes of the numerical simulation demonstrate that the amplitude ratios are significantly influenced by variable thermal conductivity, nonlocal parameters and viscosity. It is further observed from the plots that the phase speeds in a transversely isotropic medium depend on the angle of incidence. In addition, it has been established that the energy is preserved during the reflection phenomenon.

This paper first introduces the guide-weight criterion into the topology optimization problems for maximization of the fundamental eigenfrequency of vibrating continuum structures. The traditional solid isotropic material with penalization model is modified to eliminate the artificial localized modes. Based on this modified model, the iteration formula of the design variables is derived using the guide-weight criterion. An iterative mass control strategy is adopted to satisfy the equality constraint on the final mass and to stabilize the iteration process. Additionally, a mass preserving density filter based on Heaviside function is used to solve the gray transition problem. Several typical examples are used to validate the proposed method. Numerical results show that the proposed method is capable of achieving iterative convergence and clear profiles of topologies; meanwhile, the optimal results obtained by the proposed method agree well with those obtained by the commonly used bi-directional evolutionary structural optimization (BESO) method. In particular, the proposed method has a faster convergence rate than the BESO method.

A topology optimization approach based on the boundary element method (BEM) and the optimality criteria (OC) method is proposed for the optimal design of sound absorbing material distribution within sound barrier structures. The acoustical effect of the absorbing material is simplified as the acoustical impedance boundary condition. Based on the solid isotropic material with penalization (SIMP) method, a topology optimization model is established by selecting the densities of absorbing material elements as design variables, volumes of absorbing material as constraints, and the minimization of sound pressure at reference surface as design objective. A smoothed Heaviside-like function is proposed to help the SIMP method to obtain a clear 0–1 distribution. The BEM is applied for acoustic analysis and the sensitivities with respect to design variables are obtained by the direct differentiation method. The Burton–Miller formulation is used to overcome the fictitious eigen-frequency problem for exterior boundary-value problems. A relaxed form of OC is used for solving the optimization problem to find the optimal absorbing material distribution. Numerical tests are provided to illustrate the application of the optimization procedure for 2D sound barriers. Results show that the optimal distribution of the sound absorbing material is strongly frequency dependent, and performing an optimization in a frequency band is generally needed.

As the capabilities of additive manufacturing techniques increase, topology optimization provides a promising approach to design geometrically sophisticated structures. Traditional topology optimization methods aim at finding conceptual designs, but they often do not resolve sufficiently the geometry and the structural response such that the optimized designs can be directly used for manufacturing. To overcome these limitations, this paper studies the viability of the extended finite element method (XFEM) in combination with the level-set method (LSM) for topology optimization of three dimensional structures. The LSM describes the geometry by defining the nodal level set values via explicit functions of the optimization variables. The structural response is predicted by a generalized version of the XFEM. The LSM–XFEM approach is compared against results from a traditional Solid Isotropic Material with Penalization method for two-phase “solid–void” and “solid–solid” problems. The numerical results demonstrate that the LSM–XFEM approach describes crisply the geometry and predicts the structural response with acceptable accuracy even on coarse meshes.

This paper puts forward a new version of the Isotropic Material Design method for the optimum design of structures made of an elasto-plastic material within the Hencky-Nadai-Ilyushin theory. This method provides the optimal layouts of the moduli of isotropy to make the overall compliance minimal. Thus, the bulk and shear moduli are the only design variables, both assumed as non-negative fields. The trace of the Hooke tensor represents the unit cost of the design. The yield condition is assumed to be independent of the design variables, to make the design process as simple as possible. By eliminating the design variables, the optimum design problem is reduced to the pair of the two mutually dual Linear Constrained Problems (LCP). The solution to the LCP stress-based problem directly determines the layout of the optimal moduli. A numerical method has been developed to construct approximate solutions, which paves the way for constructing the final layouts of the elastic moduli. Selected illustrative solutions are reported, corresponding to various data concerning the yield limit and the cost of the design. The yield condition introduced in this paper results in bounding the values of the optimal moduli in the places of possible stress concentration, such as reentrant corners.

Shape memory polymers have received widespread attention from researchers because of their low density, shape variety, responsiveness to the environment, and transparency. This study deals with heat-shape memory polymers (SMPs) based on polylactic acid (PLA) for designing and fabricating a novel porous vascular scaffold to treat vascular restenosis. The solid isotropic material penalization method (SIMP) was applied to optimize the vascular scaffolds. Based on the torsional torque loading of Hyperworks Optistruct and the boundary conditions, the topological optimization model of a vascular scaffold unit was established. Forward and reverse hybrid modeling technology was applied to complete the final stent structure’s assembly. The glass transition temperature for the present SMPs is 42.15 °C. With the increase in temperature, the ultimate tensile strength of the SMPs is reduced from 29.5 MPa to 11.6 MPa. The maximum modulus at room temperature was around 34 MPa. Stress relaxation curves show that the material classification is a “thermoset” polymer. The superb mechanical properties, the transition temperature of the SMPs, and the recovery ratio made it a feasible candidate for a vascular scaffold. A circular tube based on the shape memory polymers was presented as an example for analyzing the recovery ratio in an unfolding state. A higher recovery ratio was obtained at a temperature of 65 °C with a tube thickness of 2 mm. Finally, the proposed porous vascular scaffold was successfully fabricated, assessed, and compared with the original and previously developed vascular scaffolds. The proposed scaffold structure regains its initial shape with a recovery ratio of 98% (recovery temperature of 47 °C) in 16 s. The tensile strength, Young’s modulus, and bending strength of the proposed scaffold were 29.5 MPa, 695.4 MPa, and 6.02 MPa, respectively. The results showed that the proposed scaffold could be regarded as a potential candidate for a vascular implantation.