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In this study, a maximum volume sampling model is proposed to improve the accuracy and efficiency of reliability computation. An ellipsoid is constructed with the maximum volume approach in a safe domain, and a new maximum volume optimization method is proposed. The sampling model only computes the samples outside the ellipsoid, which considerably enhances computational efficiency. Furthermore, the uniform sampling strategy and Givens transformation are adopted to efficiently solve the maximum volume optimization model. A series system example, a three-dimensional rock slope example, and an arch bridge example are tested to verify the validity of the proposed maximum volume sampling model. The results indicate that the maximum volume sampling model displays high accuracy and efficiency.

This paper presents a new four variable displacement model for thick-faced sandwich beams based on a layerwise formulation of transverse shear stress field. To account for structural characteristic...

This article presents continuous interlaminar shear stress analysis of laminated beams with functionally graded single-walled carbon nanotube reinforced composite (FG-CNTRC) layers based on an exte...

In this paper, the isogeometric dual reciprocity boundary element method (IG-DRBEM) is proposed to solve three-dimensional transient heat conduction problems. It is well known that the error of traditional BEM mainly comes from element dispersion, and the introduction of isogeometric ideas makes BEM become a veritable high-precision numerical method. At present, most of the problems solved by isogeometric BEM (IGBEM) are time-independent. The reason is similar to the traditional BEM, which cannot avoid solving domain integrals when solving time-dependent problems. In this paper, based on the potential fundamental solution the boundary-domain integral equation is obtained by the weighted residual method, where the classic dual reciprocity method is adopted to transform domain integrals into boundary integrals. Meanwhile, a two-level time integration scheme is used to solve the discretized differential equations. In addition, the adaptive integration scheme, the radial integral transform method and the power series expansion method are adopted to solve the boundary regular, nearly singular and singular integrals. Several classical numerical examples show that the presented method has good numerical stability and high precision by considering different factors such as the approximation function, the time step, the number of interior points and so on.

Reliability-based design optimization (RBDO) offers a powerful tool to deal with the structural design with heterogeneous interval parameters concurrently. However, it is time-consuming in the practical engineering design. Therefore, a novel sequential moving asymptote method (SMAM) is proposed to improve the computational efficiency for convex model in this study, in which the nested double-loop optimization problem is decoupled to a sequence of deterministic suboptimization problems based on the method of moving asymptotes. In addition, the sensitivity of reliability index is derived, so the finite difference for the nested optimization loop can be avoided to tremendously improve the computational efficiency. Then, the accuracy of the SMAM is proved based on the error analysis. Furthermore, the Kreisselmeier-Steinhauser (KS) function is used to assemble the multiple constraints to deal with the parallel and series RBDO problems. One benchmark mathematical example, three numerical examples, and one complex civil engineering example, i.e., tower crane, are tested to demonstrate the efficiency of the proposed method by comparison with other existing methods, and the results indicate that SMAM offers a general and effective tool for non-probabilistic reliability analysis and optimization.

This paper presents a high-order layerwise theoretical framework for laminated composite beams based on a piecewise description of the transverse shear-stress field. Linear and quadratic variations...

Most previous studies of viscoelastic sandwich plates were based on the assumption that damping was only resulting from shear deformation in the viscoelastic core. However, extensive and compressiv...

This paper develops a novel and strong adaptive piecewise model order reduction (PMOR) method for large-scale dynamical systems with viscoelastic damping. Based on polynomial least squares approximations, the system is piecewise approximated by several k t h -order ( k ≥ 2 ) dynamical systems in a wide target frequency band, in which the orders are adaptively determined with a curvature-based method. Then the convergent reduced-order models (ROMs) of the approximate systems are obtained gradually. In the above process, for each approximate system, the orthonormal basis is constructed iteratively via the k t h -order Arnoldi method to span a projection subspace. To accelerate the convergence, an influence coefficient method and an order-dependent method are proposed to automatically determine the initial order of the ROM and the order increments, respectively. More importantly, a proposed error estimation strategy can predict all forms of estimated relative errors. According to the study of these forms, a comparison-selection method is presented to determine the final ROM for the whole target band interval by interval. Four examples comprehensively validate the strong adaptive ability, high efficiency and wide applicability of the PMOR method.

In the past decades, many researches have been done on the design optimization of low- and high-frequency vibro-acoustic systems. However, the work of mid-frequency vibro-acoustic systems was rarely reported. As an improved statistical energy analysis (SEA), statistical modal energy distribution analysis (SmEdA) is based on the power balance between modes in different subsystems and extends SEA to mid-frequency range. In this article, an optimization procedure for mid-frequency vibro-acoustic systems based on SmEdA is presented. First, a vibro-acoustic system can be decoupled by using the dual-modal formulation (DMF) into a structural subsystem and an acoustic subsystem. Then, the optimization model is built by designating the total energy of the acoustic subsystem as objective function and the structural thicknesses as design variables. Finally, the optimal solution is obtained by using the method of moving asymptotes (MMA) which need to be provided with the gradient information of the objective and constraint functions in each iteration. Therefore, a sensitivity analysis about the total energy of the acoustic subsystem with respect to the thicknesses of the structures surrounding the interior acoustic cavity is performed by adopting a semi-analytical method. Moreover, a coefficient condensation technique is introduced in the sensitivity analysis to avoid the dimensional inconformity of the coefficient matrices in SmEdA due to the variation of the number of modes with the perturbation of structural sizes. Numerical examples are given to validate the effectiveness of the optimization procedure.

Most research about vibro-acoustic optimization focuses on the reduction of the global acoustic response in mid- and even high-frequency ranges. The noise control in concerned local domains inside the acoustic cavity also deserves to be studied. This article deals with a local acoustic optimization in the framework of statistical modal energy distribution analysis (SmEdA) aiming at reducing the noise in concerned local domains of mid-frequency vibro-acoustic systems. As a recently proposed method, SmEdA processes modal energies of the coupled subsystems rather than the subsystem energies directly and permits extending analytical frequency to mid-frequency range. Using a post-processing technique, the local information involving the distributions of kinetic and potential energies inside the acoustic cavity can be estimated. In the optimization model, the acoustic energy in concerned local domains of the cavity is taken as the objective function, considering the constraint on structural weight. By optimizing the thickness distribution of the structural subsystem, the local acoustic response is significantly reduced. The effectiveness of the optimization procedure and the corresponding local acoustic sensitivity technique are illustrated by the given numerical examples. Optimization results indicate: (a) the developed optimization procedure is more effective in reducing the local acoustic response compared with the global acoustic optimization; (b) the modal energies including the kinetic and potential energies in the local acoustic domain tend to be uniformly distributed after optimization.

Constrained layer damping treatments have been widely used as an effective way for vibration control and noise reduction of thin-walled plates and shells. Despite extensive application in vibration and damping analysis of sandwich plates with viscoelastic core, the rectangular element is challenged by irregular structural forms in practical engineering. In this paper, a three-layer four-node quadrilateral element with seven degrees of freedom at each node is presented. Compared with classical rectangular element, the four-node quadrilateral element has stronger adaptability in complex structural forms and boundary conditions. Based on the layer-wise theory where the constrained layer and the base layer meet Kirchhoff theory and the viscoelastic layer satisfies first-order shear deformation theory, the finite element formulation of the sandwich plate with viscoelastic core is derived by the Hamilton principle in variational form and based on the generalization of the discrete Kirchhoff Quadrilateral plate element. The complex modulus model is employed to describe the viscoelastic core of sandwich plates, allowing for the material’s frequency dependent characteristics. The natural frequencies and associated modal loss factors are computed based on the complex eigenvalue problems. The frequency dependent characteristic of the viscoelastic core is considered and an iterative procedure is introduced to solve the nonlinear eigenvalue problem. At last, six verification numerical examples that include three sandwich beam-plates and three sandwich plates are provided to compare present method with experiment, analytical method, Galerkin method, finite element methods and commercial software (NASTRAN). The results show that the proposed finite element can accurately and efficiently simulate the sandwich plates treated with constrained layer damping with a variety of structural forms and boundary conditions.

To solve challenging optimization problems with time-consuming objective and constraints, a novel efficient Kriging-based constrained optimization (EKCO) algorithm is proposed in this paper. The EKCO mainly consists of three sampling phases. In phase I of EKCO, considering the significance of constraints, feasible region is constructed via employing a feasible region sampling (FRS) criterion. The FRS criterion can avoid the local clustering phenomenon of sample points. Therefore, phase I is also a global sampling process for the objective function in the feasible region. However, the objective function may be higher-order nonlinear than constraints. In phase II, by maximizing the prediction variance of the surrogate objective, more accurate objective function in the feasible region can be obtained. After global sampling, to accelerate the convergence of EKCO, an objective local sampling criterion is introduced in phase III. The verification of the EKCO algorithm is examined on 18 benchmark problems by several recently published surrogate-based optimization algorithms. The results indicate that the sampling efficiency of EKCO is higher than or comparable with that of the recently published algorithms while maintaining the high accuracy of the optimal solution, and the adaptive ability of the proposed algorithm also be validated. To verify the ability of EKCO to solve practical engineering problems, an optimization design problem of aeronautical structure is presented. The result indicates EKCO can find a better feasible design than the initial design with limited sample points, which demonstrates practicality of EKCO.

This paper proposes a new third-order zigzag model for asymmetric and symmetric laminated composite beams. In the framework of a general displacement form, a new zigzag shear strain shape function with layerwise coefficients corresponding to constant, linear, quadratic and cubic terms is proposed. By comparing transverse shear stress fields obtained by constitutive and equilibrium equations respectively, layerwise constants of quadratic and cubic terms are determined. With further consideration of interlaminar continuity and free stress conditions on traction free surfaces, other coefficients are achieved. As interlaminar continuity and dissimilar characteristics between layers are fully considered, the present model which has only three unknowns can accurately describe zigzag effects and provide C z 0 quadratic distribution results of transverse shear stress field by constitutive equations directly. Characteristics and advantages of the present model are discussed by comparing with other classical theoretical models. Moreover, governing equations are formulated using the principle of minimum potential energy, and analytical and finite element solutions for static analysis of laminated beams are presented. Lastly, numerical validations are presented, and comparisons with exact solutions, other theoretical models and high-fidelity finite element models well demonstrate accuracy and effectiveness of the present model for laminated beams with different features.

Experimental and numerical studies are performed on perforation of carbon fiber-wound composite cylinders struck by hemispherical and conical-nosed impactors. Drop-hammer impact tests are conducted at the impact velocity of 4.5 m/s and the impact energy of 405 J. The damage morphologies and failure mechanisms of the cylinders are then analyzed. The change laws of the impact responses and the absorbed energies of the cylinders impacted by impactors with different nose-shapes are revealed. A finite element model considering both the progressive damage constitutive relation of the composite with various failure modes and the cohesive elements for the interfaces is proposed to simulate the impact events. The model predictions are found to be in good agreement with the test results. The influences of the cohesive elements on the impact behavior of the cylinder are analyzed. The present investigation is helpful for the safety assessments of the cylinders subjected to foreign object impacts.

In this paper, a new layout optimization technique is integrated with a statistical modal energy distribution analysis (SmEdA) model to obtain the optimal layout of a porous sound-absorbing material for noise control in mid-frequency vibro-acoustic systems. The considered optimization problem is minimizing the total energy of the internal acoustic cavity within the prescribed frequency range by reasonably positioning porous sound-absorbing material patches under a given volume constraint. The principle of SmEdA is based on the power balance between different modes of coupled structural and acoustic subsystems. A modal strain and kinetic energy (MSKE) method is employed to estimate the acoustic modal damping loss factors that are associated with the energy attenuation between different modes of the coupled subsystems. The developed real-valued optimization formulation provides the feasibility of adopting an accurate sensitivity analysis technique, the complex variable method (CVM). The effectiveness of the optimization procedure is demonstrated through a significant reduction in the total acoustic energy. Additionally, some conclusions with realistic significance are obtained: (a) The optimal material layout creates a more uniform distribution of modal energies in the SmEdA model; (b) The acoustic modes tend to move out of the prescribed frequency band through optimization.

Composite structures integrated with viscoelastic materials are becoming more and more popular in the application of vibration suppression. This paper presents a comprehensive approach for analyzing this class of structures with an improved Burgers model, from material constitutive modeling, finite element formulation to solution method. The refined model consists of a spring component and multiple classical Burgers components in parallel, where the spring component converts the viscoelastic fluid model to a viscoelastic solid model and the multiple Burgers components increase the accuracy. Through the introduction of auxiliary coordinates, the model is applied to the finite element formulation of composites structures with viscoelastic materials. Consequently, a complicated Volterra integro-differential equation is transformed into a standard second-order differential equation and solution techniques for linear elastic structures can be directly used for elastic–viscoelastic composite structures. The improved Burgers model is a second-order mini-oscillator model, in which every mini-oscillator term has four parameters. The model parameters determination is performed by optimization algorithm. By comparison of model fitting results for a typical viscoelastic material, the refined model is better in accuracy than Golla–Hughes–McTavish (GHM) model and original Burgers model. Finally, several numerical examples are presented to further verify the effectiveness of the improved Burgers model.