Static Analysis of Anisotropic Doubly-Curved Shell Subjected to Concentrated Loads Employing Higher Order Layer-Wise Theories

In the presentmanuscript,a Layer-Wise(LW)generalizedmodel is proposed for the linear static analysis of doublycurved shells constrained with general boundary conditions under the influence of concentrated and surface loads.The unknown field variable is modelled employing polynomials of various orders,each of them defined within each layer of the structure.As a particular case of the LW model,an Equivalent Single Layer(ESL)formulation is derived too.Different approaches are outlined for the assessment of external forces,as well as for non-conventional constraints.The doubly-curved shell is composed by superimposed generally anisotropic laminae,each of them characterized by an arbitrary orientation.The fundamental governing equations are derived starting from an orthogonal set of principal coordinates.Furthermore,generalized blending functions account for the distortion of the physical domain.The implementation of the fundamental governing equations is performed bymeans of the Generalized Differential Quadrature(GDQ)method,whereas the numerical integrations are computed employing theGeneralized IntegralQuadrature(GIQ)method.In the post-processing phase,an effective procedure is adopted for the reconstruction of stress and strain through-the-thickness distributions based on the exact fulfillment of three-dimensional equilibrium equations.A series of systematic investigations are performed in which the static response of structures with various curvatures and lamination schemes,calculated by the present methodology,have been successfully compared to those ones obtained fromrefined finite element three-dimensional simulations.Even though the present LW approach accounts for a two-dimensional assessment of the structural problem,it is capable of well predicting the three-dimensional response of structures with different characteristics,taking into account a reduced computational cost and pretending to be a valid alternative to widespread numerical implementations.

Deformation Analysis and Fixture Design of Thin-walled Cylinder in Drilling Process Based on TRIZ Theory

Thin-walled cylindrical workpiece is easy to deform during machining and clamping processes due to the insufficient rigidi.Moreover,it’s also difficult to ensure the perpendicularity of flange holes during drilling process.In this paper,the element birth and death technique is used to obtain the axial deformation of the hole through finite element simulation.The measured value of the perpendicularity of the hole was compared with the simulated value to verify then the rationality of the simulation model.To reduce the perpendicularity error of the hole in the drilling process,the theory of inventive principle solution(TRIZ)was used to analyze the drilling process of thin-walled cylinder,and the corresponding fixture was developed to adjust the supporting surface height adaptively.Three different fixture supporting layout schemes were used for numerical simulation of drilling process,and the maximum,average and standard deviation of the axial deformation of the flange holes and their maximum hole perpendicularity errors were comparatively analyzed,and the optimal arrangement was optimized.The results show that the proposed deformation control strategy can effectively improve the drilling deformation of thin-walled cylindrical workpiece,thereby significantly improving the machining quality of the parts.

Sanders＇ Mid-long Cylindrical Shell Theory and its Application to Ocean Engineering Structures

The cylindrical shell is one of the main structural parts in ocean engineering structures.These cylinders are mostly of medium length,which means that the radius of the cross section is significantly smaller than the length of the cylindrical shell.From the viewpoint of the shell theory,they belong to the mid-long cylindrical shell category.To solve mechanical problems on this kind of structure,especially a cracked cylindrical shell,analysis based on shell theory is necessary.At present the generally used solving system for the mid-long cylindrical shell is too complicated,difficult to solve,and inapplicable to engineering.This paper introduced the Sanders' mid-long cylindrical shell theory which reduces the difficulty of the solution process,and will be suitable for solving problems with complicated boundary conditions.On this basis,the engineering applications of this theory were discussed in conjunction with the problem of a mid-long cylindrical shell having a circumferential crack.The solution process is simple,and the closed form solution can usually be found.In practical engineering applications,it gives satisfactory precision.

TRANSIENT THERMAL RESPONSE IN THICK ORTHOTROPIC HOLLOW CYLINDERS WITH FINITE LENGTH:HIGH ORDER SHELL THEORY

The transient thermal response of a thick orthotropic hollow cylinder with finite length is studied by a high order shell theory. The radial and axial displacements are assumed to have quadratic and cubic variations through the thickness, respectively. It is important that the radial stress is approximated by a cubic expansion satisfying the boundary conditions at the inner and outer surfaces, and the corresponding strain should be least-squares compatible with the strain derived from the strain-displacement relation. The equations of motion are derived from the integration of the equilibrium equations of stresses, which are solved by precise integration method （PIM）. Numerical results are.obtained, and compared with FE simulations and dynamic thermo-elasticity solutions, which indicates that the high order shell theory is capable of predicting the transient thermal response of an orthotropic （or isotropic） thick hollow cylinder efficiently, and for the detonation tube of actual pulse detonation engines （PDE） heated continuously, the thermal stresses will become too large to be neglected, which are not like those in the one time experiments with very short time.

Effective-Medium Theory for Two-Phase Random Composites with and Interfacial Shell

According to the Bruggeman theory and Maxwell-Garnett theory, the effective dielectric constant of a two-phase random composite with an interfacial shell is presented. The nonlinearity of the theory is obvious. Especially, the theory is suited to study the dielectric properties of two-phase random composites with a spherical interfacial shell. The theoretical results on dielectric properties of polystyrene-barium titanate composites with an interfacial shell are in good agreement with experimental data.

Pure Membrane,Pseudo Membrane,and Semi Membrane Shell Theories of Hybrid Anisotropic Materials

Pure,pseudo and semi membrane theories may sound similar but totally different theories as well as its behavior.The differences are more significant when it comes to hybrid anisotropic materials,namely laminated shell wall thickness.The nomenclatures and classifications have been existed centuries for isotropic material shells since Donnell and Vlasov era.The methods of formulation of the theories are unique and never been used by others except by the authors.Governing differential equations are uniquely formulated for each theory by use of asymptotic expansion method which has never been used by others for isotropic or anisotropic materials.Longitudinal(L)and circumferential(Πor l)length scale were introduced during the course of asymptotic expansion method and the different theories among membrane theory are apparently classified.Characteristic behaviors of each theory are shown.

A DONNELL TYPE THEORY FOR FINITE DEFLECTION OF STIFFENED THIN CONICAL SHELLS COMPOSED OF COMPOSITE MATERIALS

A Donnell type theory is developed for finite deflection of closely stiffened truncated laminated composite conical shells under arbitrary loads by using the variational calculus and smeared-stiffener theory. The most general bending-stretching coupling and the effect of eccentricity of stiffeners are considered. The equilibrium equations, boundary conditions and the equation of compatibility are derived. The new equations of the mixed-type of stiffened laminated composite conical shells are obtained in terms of the transverse deflection and stress function. The simplified equations are also given for some commonly encountered cases.

Elastoplastic analysis of thin-walled structures in reservoir area

In the structural design of the high pier,in order to analyze the strength and structure stability,the pier was often considered a thin-walled structure.Elastoplastic incremental theory was used to establish the model of elastoplastic stability of high pier.By considering the combined action of pile,soil and pier together,the destabilization bearing capacity was calculated by using 3-D finite element method(3-D FEM) for piers with different pile and section height.Meanwhile,the equivalent stress in different sections of pier was computed and the processor of destabilization was discussed.When the pier is lower,the bearing capacity under mutual effect of pile,soil and pier is less than the situation when mutual effect is not considered;when the pier is higher,their differences are not conspicuous.Along with the increase of the cross-sectional height,the direction of destabilization bearing capacity is varied and the ultimate capacity is buildup.The results of a stability analysis example are almost identical with the practice.

STRUCTURE OF ROD SHELL THEORIES IN HILBERT SPACE

This paper builds symmetrically general theories of rods and shells under mathematical frame of 'Hilbert Space', and successfully obtains the error estimate to the system of theory.

Asymptotically Confirmed Hypotheses Method for the Construction of Micropolar and Classical Theories of Elastic Thin Shells

In the present paper asymptotic solution of boundary-value problem of three-dimensional micropolar theory of elasticity with free fields of displacements and rotations is constructed in thin domain of the shell. This boundary-value problem is singularly perturbed with small geometric parameter. Internal iteration process and boundary layers are constructed, problem of their jointing is studied and boundary conditions for each of them are obtained. On the basis of the results of the internal boundary-value problem the asymptotic two-dimensional model of micropolar elastic thin shells is constructed. Further, the qualitative aspects of the asymptotic solution are accepted as hypotheses and on the basis of them general applied theory of micropolar elastic thin shells is constructed. It is shown that both the constructed general applied theory of micropolar elastic thin shells and the classical theory of elastic thin shells with consideration of transverse shear deformations are asymptotically confirmed theories.

A General Method to Study the Sound Radiation of a Finite Cylindrical Shell Based on Elastic Theory

A general method was proposed to study the sound and vibration of a finite cylindrical shell with elastic theory. This method was developed through comprehensive analysis of the uncoupled Helmholtz equation obtained by the decomposition of elastic equations and the structure of the solution of a finite cylindrical shell analyzed by thin shell theory. The proposed method is theoretically suitable for arbitrary thickness of the shell and any frequency. Also, the results obtained through the method can be used to determine the range of application of the thin shell theory. Furthermore, the proposed method can deal with the problems limited by the thin shell theory. Additionally, the method can be suitable for several types of complex cylindrical shell such as the ring-stiffened cylindrical shell, damped cylindrical shell, and double cylindrical shell.

Powell's optimal identification of material constants of thin-walled box girders based on Fibonacci series search method

A dynamic Bayesian error function of material constants of the structure is developed for thin-walled curve box girders. Combined with the automatic search scheme with an optimal step length for the one-dimensional Fibonacci series, Powell＇s optimization theory is used to perform the stochastic identification of material constants of the thin-walled curve box. Then, the steps in the parameter identification are presented. Powell＇s identification procedure for material constants of the thin-walled curve box is compiled, in which the mechanical analysis of the thin-walled curve box is completed based on the finite curve strip element （FCSE） method. Some classical examples show that Powell＇s identification is numerically stable and convergent, indicating that the present method and the compiled procedure are correct and reliable. During the parameter iterative processes, Powell＇s theory is irrelevant with the calculation of the FCSE partial differentiation, which proves the high computation efficiency of the studied methods. The stochastic performances of the system parameters and responses axe simultaneously considered in the dynamic Bayesian error function. The one-dimensional optimization problem of the optimal step length is solved by adopting the Fibonacci series search method without the need of determining the region, in which the optimized step length lies.

Peridynamic Modeling of Brittle Fracture in Mindlin-Reissner Shell Theory

In this work,wemodeled the brittle fracture of shell structure in the framework of Peridynamics Mindlin-Reissener shell theory,in which the shell is described by material points in themean-plane with its drilling rotation neglected in kinematic assumption.To improve the numerical accuracy,the stress-point method is utilized to eliminate the numerical instability induced by the zero-energy mode and rank-deficiency.The crack surface is represented explicitly by stress points,and a novel general crack criterion is proposed based on that.Instead of the critical stretch used in common peridynamic solid,it is convenient to describe thematerial failure by using the classic constitutive model in continuum mechanics.In this work,a concise crack simulation algorithm is also provided to describe the crack path and its development,in order to simulate the brittle fracture of the shell structure.Numerical examples are presented to validate and demonstrate our proposed model.Results reveal that our model has good accuracy and capability to represent crack propagation and branch spontaneously.

Are “Higher-Order” and “Layer-wise Zig-Zag” Plate & Shell Theories Necessary for Functionally Graded Materials and Structures?

Similar to the very vast prior literature on analyzing laminated composite structures,“higher-order”and“layer-wise higher-order”plate and shell theories for functionally-graded(FG)materials and structures are also widely popularized in the literature of the past two decades.However,such higher-order theories involve(1)postulating very complex assumptions for plate/shell kinematics in the thickness direction,(2)defining generalized variables of displacements,strains,and stresses,and(3)developing very complex governing equilibrium,compatibility,and constitutive equations in terms of newly-defined generalized kinematic and generalized kinetic variables.Their industrial applications are thus hindered by their inherent complexity,and the fact that it is difficult for end-users(front-line structural engineers)to completely understand all the newly-defined generalized DOFs for FEM in the higher-order and layer-wise theories.In an entirely different way,very simple 20-node and 27-node 3-D continuum solid-shell elements are developed in this paper,based on the simple theory of 3D solid mechanics,for static and dynamic analyses of functionally-graded plates and shells.A simple Over-Integration(a 4-point Gauss integration in the thickness direction)is used to evaluate the stiffness matrices of each element,while only a single element is used in the thickness direction without increasing the number of degrees of freedom.A stress-recovery approach is used to compute the distribution of transverse stresses by considering the equations of 3D elasticity in Cartesian as well as cylindrical polar coordinates.Comprehensive numerical results are presented for static and dynamic analyses of FG plates and shells,which agree well,either with the existing solutions in the published literature,or with the computationally very expensive solutions obtained by using simple 3D isoparametric elements(with standard Gauss Quadrature)available in NASTRAN(wherein many 3D elements are used in the thickness direction to capture the varying material properties).The effects of the material gradient index,the span-to-thickness ratio,the aspect ratio and the boundary conditions are also studied in the solutions of FG structures.Because the proposed methodology merely involves:(2)standard displacement DOFs at each node,(2)involves a simple 4-point Gaussian over-integration in the thickness direction,(3)relies only on the simple theory of solid mechanics,and(4)is capable of accurately and efficiently predicting the static and dynamical behavior of FG structures in a very simple and cost-effective manner,it is thus believed by the authors that the painstaking and cumbersome development of“higher-order”or“layer-wise higher-order”theories is not entirely necessary for the analyses of FG plates and shells.

A nonlinear explicit dynamic GBT formulation for modeling impact response of thin-walled steel members

A nonlinear explicit dynamic finite element formulation based on the generalized beam theory(GBT)is proposed and developed to simulate the dynamic responses of prismatic thin-walled steel members under transverse impulsive loads.Considering the rate strengthening and thermal softening effects on member impact behavior,a modified Cowper-Symonds model for constructional steels is utilized.The element displacement field is built upon the superposition of GBT cross-section deformation modes,so arbitrary deformations such as cross-section distortions,local buckling and warping shear can all be involved by the proposed model.The amplitude function of each cross-section deformation mode is approximated by the cubic non-uniform B-spline basis functions.The Kirchhoff s thin-plate assumption is utilized in the construction of the bending related displacements.The Green-Lagrange strain tensor and the second Piola-Kirchhoff(PK2)stress tensor are employed to measure deformations and stresses at any material point,where stresses are assumed to be in plane-stress state.In order to verify the effectiveness of the proposed GBT model,three numerical cases involving impulsive loading of the thin-walled parts are given.The GBT results are compared with those of the Ls-Dyna shell finite element.It is shown that the proposed model and the shell finite element analysis has equivalent accuracy in displacement and stress.Moreover,the proposed model is much more computationally efficient and structurally clearer than the shell finite elements.

THE RATIONALISM THEORY AND ITS FINITE ELEMENT ANALYSIS METHOD OF SHELL STRUCTURES

In this paper, a kind of rationalism theory of shell is established which is of different mechanic characters in tension and in compression, and the finite element numerical analysis method is also described.

弹性环梁支撑下圆形深基坑支护结构变形解析解

将环梁和支护结构分别视为弹性圆环和弹性圆柱薄壳,基于环梁和圆柱壳的变形协调,得到了具有任意数目弹性环梁支撑圆形深基坑支护结构变形的解析解.在验证解析解合理性和可靠性的基础上,针对某一实际圆形基坑工程,比较了在刚性和弹性环梁支撑下支护结构变形和内力的差异,并分析了支护结构底部边界条件、环梁弹性模量、尺寸和数量以及位置等参数对支护结构变形和内力分布的影响.研究结果表明:相对于刚性环梁支撑,弹性环梁支撑处内力变化较小,环梁弹性模量和尺寸的改变只对基坑挖掘面以上支护结构变形和内力影响显著,而对挖掘面以下的支护结构变形和内力几乎没有影响.该研究成果为圆形基坑支护结构设计提供了理论依据和指导.

超协调元

该文提出一类超协调的单元理论。不同于在普通协调元中采用的线位移协调插值格式,超协调元的单元插值函数首先引入转角自由度等线位移导数的高阶协调假设,并通过积分推导,进而获得超协调的线位移模型。基于超协调元理论,该文构造了一类新型的三结点三角形平板壳元SCT。数值算例表明:与其他类型单元相比,基于超协调元理论的单元具有计算精度高和计算效率好的优势。该文所提出单元理论构造简单,超协调元理论可以成为构造高性能数值算法的一种新的通用理论。

圆形基坑极正交各向异性支护结构变形解析分析

考虑圆形深基坑支护结构轴向和环向配筋的差异,将支护结构简化为极正交各向异性圆柱薄壳,研究了分层土体中具有弹性支撑环梁约束的支护结构轴对称变形和内力特征.首先,将弹性支撑环梁的约束解除,代之以沿环向分布的未知集中力,基于弹性环梁和圆柱壳的边界条件和变形协调条件,得到了分层土体中具有弹性支撑环梁支护结构轴对称变形的解析解.其次,以上海地区某一圆形深基坑支护结构为例,揭示了支护结构环向和纵向弹性模量、环梁刚度、土体重度和静止土压力系数等因素对支护结构内力和变形的影响,结果表明:支护结构以环向承压为主,轴向弯曲为辅,故其环向刚度对径向位移的影响要明显大于其轴向刚度的影响,但材料参数对内力分布影响较弱;环梁刚度的增加可有效限制支护结构的变形,但会引起支护结构在支撑环梁处内力的显著增大;土层性质相差不大区域的支护结构可按均质土中支护结构进行分析,而土层性质有较大突变区域的支护结构分析则需考虑土层的分层效应.

基于薄膜壳体理论的仿淋巴瓣膜结构设计

淋巴系统中的瓣膜结构是控制淋巴液单向流动的关键结构,进而影响肿瘤细胞的淋巴转移过程。基于薄膜壳体理论设计了仿淋巴瓣膜结构,通过COMSOL有限元仿真分析了瓣膜厚度、弹性对其变形的影响。配制了聚二甲基硅氧烷(PDMS)与Ecoflex00—30的混合材料,通过调整二者的体积比,使其杨氏模量与生物组织实际值更接近。采用软刻蚀技术制作了仿淋巴管微通道,测试了其单向截流性能。结果表明:在80 Pa压力下,仿淋巴瓣膜结构无明显漏液现象,单向截流性能良好。