An investigation on multilayer shape memory polymers under finite bending through nonlinear thermo-visco-hyperelasticity

This study presents a semi-analytical solution to describe the behavior of shape memory polymers(SMPs) based on the nonlinear thermo-visco-hyperelasticity which originates from the concepts of internal state variables and rational thermodynamics. This method is developed for the finite bending of multilayers in a dual-shape memory effect(SME) cycle. The layer number and layering order are investigated for two different SMPs and a hyperelastic material. In addition to the semi-analytical solution...     

Swelling-induced ?nite bending of functionally graded p H-responsive hydrogels: a semi-analytical method

Recently, pH-sensitive hydrogels have been utilized in the diverse applications including sensors, switches, and actuators. In order to have continuous stress and deformation ?elds, a new semi-analytical approach is developed to predict the swelling induced?nite bending for a functionally graded(FG) layer composed of a pH-sensitive hydrogel,in which the cross-link density is continuously distributed along the thickness direction under the plane strain condition. Without considering the intermediary virtual reference,the initial state is mapped into the deformed con?guration in a circular shape by utilizing a total deformation gradient tensor stemming from the inhomogeneous swelling of an FG layer in response to the variation of the pH value of the solvent. To enlighten the capability of the presented analytical method, the ?nite element method(FEM) is used to verify the accuracy of the analytical results in some case studies. The perfect agreement con-?rms the accuracy of the presented method. Due to the applicability of FG pH-sensitive hydrogels, some design factors such as the semi-angle, the bending curvature, the aspect ratio, and the distributions of deformation and stress ?elds are studied. Furthermore, the tangential free-stress axes are illustrated in deformed con?guration.     

A nonlinear,transient finite element method for coupled solvent diffusion and large deformation of hydrogels

Hydrogels are capable of coupled mass transport and large deformation in response to external stimuli. In this paper, a nonlinear, transient finite element formulation is presented for initial boundary value problems associated with swelling and deformation of hydrogels, based on a nonlinear continuum theory that is consistent with classical theory of linear poroelasticity. A mixed finite element method is implemented with implicit time integration. The incompressible or nearly incompressible behavior at the initial stage imposes a constraint to the finite element discretization in order to satisfy the Ladyzhenskaya–Babuska–Brezzi (LBB) condition for stability of the mixed method, similar to linear poroelasticity as well as incompressible elasticity and Stokes flow; failure to choose an appropriate discretization would result in locking and numerical oscillations in transient analysis. To demonstrate the numerical method, two problems of practical interests are considered: constrained swelling and flat-punch indentation of hydrogel layers. Constrained swelling may lead to instantaneous surface instability for a soft hydrogel in a good solvent, which can be regulated by assuming a stiff surface layer. Indentation relaxation of hydrogels is simulated beyond the linear regime under plane strain conditions, in comparison with two elastic limits for the instantaneous and equilibrium states. The effects of Poisson’s ratio and loading rate are discussed. It is concluded that the present finite element method is robust and can be extended to study other transient phenomena in hydrogels.     

On the influence of interfacial properties to the bending rigidity of layered structures

Layered structures are ubiquitous, from one-atom thick layers in two-dimensional materials, to nanoscale lipid bi-layers, and to micro and millimeter thick layers in composites. The mechanical behavior of layered structures heavily depends on the interfacial properties and is of great interest in engineering practice. In this work, we give an analytical solution of the bending rigidity of bilayered structures as a function of the interfacial shear strength. Our results show that while the critical bending stiffness when the interface starts to slide plastically is proportional to the interfacial shear strength, there is a strong nonlinearity between the rigidity and the applied bending after interfacial plastic shearing. We further give semi-analytical solutions to the bending of bilayers when both interfacial shearing and pre-existing crack are present in the interface of rectangular and circular bilayers. The analytical solutions are validated by using finite element simulations. Our analysis suggests that interfacial shearing resistance, interfacial stiffness and preexisting cracks dramatically influence the bending rigidity of bilayers. The results can be utilized to understand the significant stiffness difference in typical biostructures and novel materials, and may also be used for non-destructive detection of interfacial crack in composites when stiffness can be probed through vibration techniques.     

Bonded lap joints of composite laminates with tapered edges

This study presents a semi-analytical solution method to analyze the geometrically nonlinear response of bonded composite lap joints with tapered and/or non tapered adherend edges under uniaxial tension. The solution method provides the transverse shear and normal stresses in the adhesives and in-plane stress resultants and bending moments in the adherends. The method utilizes the principle of virtual work in conjunction with von Karman’s nonlinear plate theory to model the adherends and the shear lag model to represent the kinematics of the thin adhesive layers between the adherends. Furthermore, the method accounts for the bilinear elastic material behavior of the adhesive while maintaining a linear stress–strain relationship in the adherends. In order to account for the stiffness changes due to thickness variation of the adherends along the tapered edges, the in-plane and bending stiffness matrices of the adherents are varied as a function of thickness along the tapered region. The combination of these complexities results in a system of nonlinear governing equilibrium equations. This approach represents a computationally efficient alternative to finite element method. The numerical results present the effects of taper angle, adherend overlap length, and the bilinear adhesive material on the stress fields in the adherends, as well as the adhesives of a single- and double-lap joint.     

流固耦合的周期加强板的振动及声辐射研究

研究了流体负载下的无穷大双周期加强板, 在周期谐振力作用下的振动响应和声辐射,并提出了一种基于有限元和空间波数法的半解析半数值方法. 首先利用有限元的方法对周期结构进行单元离散, 并将结构对薄板的作用力等效为节点力的作用. 然后通过周期结构的振动方程, 结合薄板与结构的位移边界条件, 建立了节点力与薄板节点位移的函数方程. 最后应用空间波数法和傅里叶变换, 并采用数值计算的方法求解出薄板的节点位移, 得到了周期加强板关于离散节点位移的振动和辐射声压方程. 在数值算例中, 对该方法的正确性进行了验证, 并且分析了周期结构对薄板的振动和声辐射的影响.     

Postbuckling of long unsymmetrically laminated composite plates under axial compression

An approximate solution is given for the postbuckling of infinitely long and unsymmetrically laminated composite plates. This solution is obtained by superposing a polynomial transverse displacement given by bending due to unsymmetric laminate configurations and a simple functional representation for the buckling mode in conjunction with the Galerkin method. Nondimensional parameters are used to express the approximate solution in a very simple and clear formulation. The results given by this solution for axial compression in the longitudinal direction are compared with the results given by the nonlinear finite element method (FEM) for finite length rectangular long plates. The influence of the boundary conditions on postbuckling response is also studied. For the FEM analysis, two different simply supported boundary conditions on the long edges of the plate are considered. It is found that these two sets of boundary conditions give different results for the buckling and postbuckling finite element analysis. In most cases the FEM analysis overestimate and, respectively, underestimate the approximate closed form solution, depending on the type of simply supported boundary condition considered. Thus, the approximate solution appears useful for design purposes as an averaged quantity between the two FEM analyses. Also, it is found that the reduced bending stiffness method can be successfully used for determining the approximate solution.     

PRECISE INTEGRAL ALGORITHM BASED SOLUTION FOR TRANSIENT INVERSE HEAT CONDUCTION PROBLEMS WITH MULTI-VARIABLES

IntroductionIHCPs (InverseHeatConductionProblems)arecloselyassociatedwithmanyengineeringaspects,andwelldocumentedintheliteratures,coveringtheidentificationsofthermalparameters[1,2 ],boundaryshapes[3],boundaryconditions[4 ]andsource_relatedterms[5 ,6 ]etc .Howeveritseemsthatonlylittleworkisdirectlyconcernedwithmulti_variablesidentificationsbyauthors’knowledge.Tsengetal.presentedanapproachtodeterminingtwokindsofvariables[7],butonlygavefewnumericalexamplestodeterminethemsimultaneously .Thesol…     

考虑进油压力的滑动轴承非线性油膜力数据库

通过对ReyTlolds方程的非线性变换，提出了考虑进油压力边界条件时径向滑动轴承非线性油膜力数据库的建库方法，扩展了油膜力数据库计算方法的应用，通过引入2个有限数据域的新变量对转子轴心速度项和进油压力边界条件进行有限化处理，得到了更符合实际工况的连续性油膜力数据库及计算模型，同有限元法对比分析了非线性油膜力数据库的适用性．结果表明，非线性油膜力数据库模型的精度较高，所建立的非线性油膜力计算模型可用于对转子系统瞬态运动进行简便和快捷的分析．     

泊松白噪声激励下强非线性系统的半解析瞬态解

自然界与工程中都普遍存在着随机扰动,且大多数呈现出固有的非高斯性质,若采用高斯激励建模可能会导致巨大的误差.泊松白噪声作为一种典型且重要的非高斯激励模型,已引起了广泛的关注.目前,泊松白噪声激励下系统的动态特性分析主要集中于稳态响应的研究,而针对瞬态响应的求解难度仍较大,需进一步发展.本文引入径向基神经网络,提出了一种泊松白噪声激励下单自由度强非线性系统瞬态响应预测的高效半解析方法.首先将广义Fokker-Plank-Kolmogorov (FPK)方程的瞬态解表示为一组含时变待定权值系数的高斯径向基神经网络;然后采用有限差分法离散时间导数项,并结合随机取样技术构造含时间递推式的损失函数;最后通过拉格朗日乘子法使得损失函数最小化获得时变最优权值系数.作为算例,探究了两个经典强非线性系统,并采用蒙特卡罗模拟方法对解析结果加以验证.结果表明:本文方法所获得的瞬时概率密度函数与蒙特卡罗模拟数据吻合地较好,并且算法具备较高的计算效率.在系统响应的整个演化过程中,本文所提方法能够非常有效地捕捉到系统响应在各个时刻下的复杂非线性特征.此外,本文方法所获得的高精度半解析瞬态解,不仅可作为基准解检验其...     

结构优化半解析灵敏度分析的改进算法

提出了结构半解析灵敏度分析的改进算法,该算法实现简便,对于设计变量摄动步长具有极佳的数值稳定特性。首先,从总体角度推导静力问题半解析法灵敏度分析新算法,提出了位移与应力灵敏度列式,并给出了算法实施途径;然后,将此思路推广于自振频率、屈曲临界荷载和瞬态响应等多种问题,提出了相应的计算步骤。以梁单元与壳单元等典型结构为例,开展了多个算例测试。测试表明,改进算法计算精度和效率均有提升,特别是设计变量步长有更大的数值稳定区域,为复杂工程结构形状优化的灵敏度分析提供了新途径。     

ELASTO-PLASTIC COUPLED ANALYSIS OF BURIED STRUCTURE AND SOIL MEDIUM BY PERTURBATIONAL SEMI-ANALYTIC METHOD

I.IntroductionMoreandmoreelasto-plasticanalysesareusedinCivilEngineering.TheMohr-Coulombyieldconditionisoftenappliedtorockandsoilmediumtostudythesituationofdestruction.Theperturbationalmethodwasfirstusedinthestudyofcelestialmechanics,thenithasbeenusedinsolidmechanicstocarryoutthegeometricallyandphysicallynonlinearanalysis[']'12].Forlarge?scalcproblems,thegeneralnumericalmethodsmaynotbeapttothiscomplexcalculation,butsemi-analyticalmethodscandoitwell.Touseanalyticalfunctionsinoneortwodirectio…     

Shaft design: A semi-analytical finite element approach

This work deals with the practical use of semi-analytical finite elements in the machine design. The case of mechanical shafts is considered. The most usual loading condition characterized by the presence of axial, torsional, bending, and shear loads can be modeled by over imposing an axi-symmetric, an axi-antisymmetric and a harmonic load, corresponding to the first three terms of the Fourier series expansion, if semi-analytical plane finite element is used. A practical case is presented and the advantages, with respect to the three-dimensional approach in terms of computational time and accuracy for stress and displacement evaluation, is put in evidence.     

Study on calculation methods for acoustic radiation of axisymmetric structures in finite water depth

In this paper, a kind of FEM–WSM (Finite Element Method–Wave​ Superposition Method) is used to calculate the acoustic radiation of axisymmetric structures in finite water depth. FEM is used to solve the dry modes of axisymmetric structures, and WSM is applied along with the dry mode method to consider fluid–structure interaction effects and calculate the acoustic radiated field. This method combines the advantages of FEM and WSM. On one hand, it is suitable for complex or large axisymmetric structures on the one hand. On the other hand, it has higher computational efficiency than the FEM, and the computational domain size for the water is not limited. As long as the Green’s function is tailored for the boundary condition, the acoustic radiated field of axisymmetric structures in more complex ocean acoustic environments can be calculated by using this method. Besides, a least-square method is used to reduce the distortion resulting from computational errors of the modal estimates. The influence of the number of source and field points and the finite element mesh density on the calculation accuracy are discussed, eliciting some disciplinary conclusions. Using a spherical shell and a capsule shell as models, the results from the present approach, a semi-analytical method, and the crude FEM are compared to verify the correctness and efficiency. Based on numerical examples, the influence of the sea surface and the seafloor on the acoustic radiated field of structures in finite water depth is also analyzed.     

Temperature stress analysis for bi-modulus beam placed on Winkler foundation

The materials with different moduli in tension and compression are called bi-modulus materials. Graphene is such a kind of materials with the highest strength and the thinnest thickness. In this paper, the mechanical response of the bi-modulus beam subjected to the temperature effect and placed on the Winkler foundation is studied. The differential equations about the neutral axis position and undetermined parameters of the normal strain of the bi-modulus foundation beam are established. Then, the analytical expressions of the normal stress, bending moment, and displacement of the foundation beam are derived. Simultaneously, a calculation procedure based on the finite element method(FEM) is developed to obtain the temperature stress of the bi-modulus structures. It is shown that the obtained bi-modulus solutions can recover the classical modulus solution, and the results obtained by the analytical expressions, the present FEM procedure, and the traditional FEM software are consistent, which verifies the accuracy and reliability of the present analytical model and procedure. Finally, the difference between the bi-modulus results and the classical same modulus results is discussed, and several reasonable suggestions for calculating and optimizing the certain bi-modulus member in practical engineering are presented.     

3D numerical simulation on fluid-structure interaction of structure subjected to underwater explosion with cavitation

In the underwater-shock environment,cavitation occurs near the structural surface.The dynamic response of fluid-structure interactions is influenced seriously by the cavitation effects.It is also the difficulty in the field of underwater explosion.With the traditional boundary element method and the finite element method(FEM),it is difficult to solve the nonlinear problem with cavitation effects subjected to the underwater explosion.To solve this problem,under the consideration of the cavitation effects and fluid compressibility,with fluid viscidity being neglected,a 3D numerical model of transient nonlinear fluid-structure interaction subjected to the underwater explosion is built.The fluid spectral element method(SEM) and the FEM are adopted to solve this model.After comparison with the FEM,it is shown that the SEM is more precise than the FEM,and the SEM results are in good coincidence with benchmark results and experiment results.Based on this,combined with ABAQUS,the transient fluid-structure interaction mechanism of the 3D submerged spherical shell and ship stiffened plates subjected to the underwater explosion is discussed,and the cavitation region and its influence on the structural dynamic responses are presented.The paper aims at providing references for relevant research on transient fluid-structure interaction of ship structures subjected to the underwater explosion.     

Nonlinear vibration analysis of isotropic cantilever plate with viscoelastic laminate

The nonlinear vibration of an isotropic cantilever plate with viscoelastic laminate is investigated in this article. Based on the Von Karman’s nonlinear geometry and using the methods of multiple scales and finite difference, the dimensionless nonlinear equations of motion are analyzed and solved. The solvability condition of nonlinear equations is obtained by eliminating secular terms and, finally, nonlinear natural frequencies and mode-shapes are obtained. Knowing that the linear vibration of this type of plate does not have exact solution, Ritz method is employed to obtain semi-analytical nonlinear mode-shapes of transverse vibration of this plate. Airy stress function and Galerkin method are employed to reduce nonlinear PDEs into an ODE of duffing type. Stability of plate and chaotic behavior are investigated by Runge–Kutta method. Poincare section diagrams are in good agreement with results of Lyapunov criteria.     

AXISYMMETRIC BENDING OF TWO-DIRECTIONAL FUNCTIONALLY GRADED CIRCULAR AND ANNULAR PLATES

Assuming the material properties varying with an exponential law both in the thick- ness and radial directions,axisymmetric bending of two-directional functionally graded circular and annular plates is studied using the semi-analytical numerical method in this paper.The de- flections and stresses of the plates are presented.Numerical results show the well accuracy and convergence of the method.Compared with the finite element method,the semi-analytical nu- merical method is with great advantage in the computational efficiency.Moreover,study on ax- isymmetric bending of two-directional functionally graded annular plate shows that such plates have better performance than those made of isotropic homogeneous materials or one-directional functionally graded materials.Two-directional functionally graded material is a potential alter- native to the one-directional functionally graded material.And the integrated design of materials and structures can really be achieved in two-directional functionally graded materials.     

半解析板－梁超级元

本文构造了一种半解析板－梁超级元，它由板－梁超级弯曲元与板－梁超级平面元组合成。由于采用解析型的梁函数作为超级元弯曲位移模式，因而这一超级元具有精度高、自由度少的优点。用超级元法对由大量板和梁构件组成的复杂结构进行整体分析、尤其是进行动力分析时，这一超级元是一种高效的单元。文中导出了这一超级元的全部列式。     

Static analysis of ultra-thin beams based on a semi-continuum model

A linear semi-continuum model with discrete atomic layers in the thickness direction was developed to investigate the bending behaviors of ultra-thin beams with nanoscale thickness.The theoretical results show that the deflection of an ultra-thin beam may be enhanced or reduced due to different relaxation coefficients.If the relaxation coefficient is greater/less than one,the deflection of micro/nano-scale structures is enhanced/reduced in comparison with macro-scale structures.So,two opposite types of size-dependent behaviors are observed and they are mainly caused by the relaxation coefficients.Comparisons with the classical continuum model,exact nonlocal stress model and finite element model (FEM) verify the validity of the present semi-continuum model.In particular,an explanation is proposed in the debate whether the bending stiffness of a micro/nano-scale beam should be greater or weaker as compared with the macro-scale structures.The characteristics of bending stiffness are proved to be associated with the relaxation coefficients.