Natural Vibrations of a Cylindrical Shell with Circular Ribs Attached by Means of Discrete Elastic Elements

The vibrations of a cylindrical shell reinforced with circular ribs attached to it by means of discrete elastic elements are studied. The problem is solved by the finite-element method. The shell and ribs are modeled by a plane four-node finite element, which is a combination of a four-node plane stress element and a four-node flexural element. The effect of the stiffness of the elastic elements on the natural frequencies and modes is examined __________ Translated from Prikladnaya Mekhanika, Vol. 41, No. 10, pp. 108–113, October 2005.     

Creep-rupture lifetime simulation of unidirectional metal matrix composites with and without time-dependent fiber breakage

A numerical simulation for predicting the axial creep-rupture lifetime of continuous fiber-reinforced metal matrix composites is proposed, based on the finite element method. The simulation model is composed of line elements representing the fibers and four-node isoparametric plane elements representing the matrix. While the fibers behave as an elastic body at all times, the matrix behaves as an elasto-plastic body at the loading process and an elasto-plastic creep body at the creep process. It is further assumed in the simulation that the fibers are fractured not only in stress criterion but time-dependently with random nature. Simulation results were compared with the creep-rupture lifetime data of a boron-aluminum composite with 10% fiber volume fraction experimentally obtained. The simulated creep-rupture lifetimes agreed well with the averages of the experimental data. The proposed simulation is further carried out to predict a possibility of creep-rupture for the composite without time-dependent fiber breakage. It is finally concluded that the creep-rupture of a boron-aluminum composite is closely related with the shear stress relaxation occurring in the matrix as well as time-dependent fiber breakage.     

The perturbation finite element method for solving the plane problem in consideration of linear creep

In this paper, a method (PFMC) for solving plane problem of linear creep is presented by using perturbation finite element. It can be used in plane problem in consideration of creep, such as reinforced concrete beam, presiressed concrete beam, reinforced concrete cylinder and reinforced concrete tunnel in elastic or visco-elastic medium, as well as underground building and so on.In the presented method, the assumption made in the general increment method that variables remain constant in a divided time interval is not taken. The accuracy is improved and the length of time step becomes larger. The computer storage can be reduced and the calculating efficiency can be increased.Perturbation finite element formulae for four-node quadrilateral isoparametric element including reinforcement are established and five numerical examples are given. As contrasted with the analytical solution, the accuracy is satisfactory.     

Boundary-type finite element method for wave propagation analysis

The boundary-type finite element method has been investigated and applied to the Helmholz and mild-slope equations. Four types of interpolation function are examined based on trigonometric function series. Three-node triangular, four-node quadrilateral, six-node triangular and eight-node quadrilateral elements are tested; these are all non-conforming elements. Three types of numerical example show that the three-node triangular and four-node quadrilateral elements are useful for practical analysis.     

A novel four-node quadrilateral element with continuous nodal stress

Formulation and numerical evaluation of a novel four-node quadrilateral element with continuous nodal stress（Q4-CNS）are presented.Q4-CNS can be regarded as an improved hybrid FE-meshless four-node quadrilateral element（FE-LSPIM QUAD4）, which is a hybrid FE-meshless method.Derivatives of Q4-CNS are continuous at nodes, so the continuous nodal stress can be obtained without any smoothing operation.It is found that,compared with the standard four-node quadrilateral element（QUAD4）,Q4- CNS can achieve significantly better accuracy and higher convergence rate.It is also found that Q4-CNS exhibits high tolerance to mesh distortion.Moreover,since derivatives of Q4-CNS shape functions are continuous at nodes,Q4-CNS is potentially useful for the problem of bending plate and shell models.     

A novel hybrid finite element analysis of inplane singular elastic field around inclusion corners in elastic media

This paper deals with the inplane singular elastic field problems of inclusion corners in elastic media by an ad hoc hybrid-stress finite element method. A one-dimensional finite element method-based eigenanalysis is first applied to determine the order of singularity and the angular dependence of the stress and displacement field, which reflects elastic behavior around an inclusion corner. These numerical eigensolutions are subsequently used to develop a super element that simulates the elastic behavior around the inclusion corner. The super element is finally incorporated with standard four-node hybrid-stress elements to constitute an ad hoc hybrid-stress finite element method for the analysis of local singular stress fields arising from inclusion corners. The singular stress field is expressed by generalized stress intensity factors defined at the inclusion corner. The ad hoc finite element method is used to investigate the problem of a single rectangular or diamond inclusion in isotropic materials under longitudinal tension. Comparison with available numerical results shows the present method is an efficient mesh reducer and yields accurate stress distribution in the near-field region. As applications, the present ad hoc finite element method is extended to discuss the inplane singular elastic field problems of a single rectangular or diamond inclusion in anisotropic materials and of two interacting rectangular inclusions in isotropic materials. In the numerical analysis, the generalized stress intensity factors at the inclusion corner are systematically calculated for various material type, stiffness ratio, shape and spacing position of one or two inclusions in a plate subjected to tension and shear loadings.     

The Stress State of Stiffened Shallow Orthotropic Shells

An approach is proposed for stress analysis of elastic systems consisting of shallow shells having a rectangular planform and stiffened with rods in one direction. The shell curvature varying in the direction perpendicular to the ribs and piecewise-constant in another direction is taken into account. A system of ordinary differential equations and shell–rib conjugation conditions are derived after separation of variables for two simply supported opposite contours. A one-dimensional boundary-value problem is solved by a stable numerical method. The results of a stress–strain analysis of shipbuilding structural elements are presented as an example     

基于Layerwise离散层理论的复合材料夹层板屈曲分析

复合材料夹层结构由于面板和芯层力学特性差异较大,屈曲分析时要分层考虑各层的剪切变形。基于Reddy的Layerwise离散层理论,假设每一层变形服从一阶剪切变形理论,在统一的位移场描述下,推导建立了一种用于复合材料夹层结构屈曲分析的四节点四边形板单元,并采用混合插值方法对单元的剪切锁定进行了修正。分别对三种典型的夹层板结构进行线性屈曲有限元分析,并将计算结果与文献中已有结果进行了对比。结果表明：本文的分析方法能离散考虑各层的力学特性,将结构离散为多层时,计算结果与三维弹性理论或高阶板理论吻合;将结构等效为单层时,计算结果与基于一阶剪切变形理论的文献结构吻合,验证了单元的有效性。     

基于加权残量法的多变量等参元简明列式及其应用

根据作者提出的建立多变量有限元模型的系统化方法，应用加权残量法的基本原理，给出了建立多变量等参元模型的简明列式。然后应用该列式，构造了简明有效的平面四结点多变量等参元MQ4和MQ5前者不含内部自由度，后者含有内部自由度。文中结合若干典型算例对所构造的单元性能进行了考核，并与若干典型协调与非协调等参元的数值结果进行了比较。数值结果表明，无论是在规则网格还是在不规则网格情况下，本文构造的多变量等参元，不仅能通过分片检验的要求，而且表现出了良好的性能。     

基于8节点平面单元的RC梁柱节点单元

为了分析RC框架结构的非线性滞回性能,基于平面8节点单元,本文提出了一个新的针对受循环荷载作用钢筋混凝土的梁柱节点单元．单元中梁与节点交界面和柱与节点交界面被划分成“节点截面”和“梁柱截面”,节点核心区的力学性能由8节点单元描述,而梁柱受力钢筋与节点核心区的粘结滑移由存在于“节点截面”和“梁柱截面”之间的8根弹簧控制,梁柱与节点之间的剪切由4根剪切弹簧表示．单元具有4个外节点和8个内节点,每个内节点具有2个自由度,每个外节点具有3个自由度,该3个自由度与普通梁单元一致,从而确保本单元能够同普通一维梁柱单元一起进行钢筋混凝土结构平面非线性分析．通过将内节点上的自由度依附到外节点上,单元在数值表现上具有4个节点和28个自由度．通过对比试验和模拟分析结果,验证了本模型适合于循环荷载作用下平面框架结构的非线性响应分析．     

前屈曲应力状态对组合加肋旋转壳失稳临界压力影响的探讨

推导了包含前屈曲弯矩和横剪力的旋转壳弹性稳定性基本方程.运用Riccati传递矩阵法对组合加肋旋转壳算例进行了稳定性分析,并与假设前屈曲状态为薄膜应力状态计算出的失稳临界压力进行了比较.结果表明,前屈曲弯矩和横剪力对组合加肋旋转壳失稳临界压力的影响较小,随着壳板厚度和肋骨尺寸的增大及肋骨间距的缩短,影响略有增大.因而,分析组合加肋旋转壳弹性稳定性时,前屈曲状态采用薄膜应力状态的假设是合理的.     

On large-strain finite element solutions of higher-order gradient crystal plasticity

A finite-strain higher-order gradient crystal plasticity model accounting for the backstress effect originating from the existence of geometrically necessary dislocations (GNDs) is applied to plane strain finite element analysis. Different element types are tested to seek out an element formulation that is reliable and useful for solving problems involving severe plastic deformation. In the present finite element formulation, the GND density rates are chosen to be additional nodal degrees of freedom. Different orders of shape functions are employed for the interpolation of displacement rates and GND density rates. Their effects on solutions are examined in detail by considering three boundary value problems: a simple shear of a constrained layer (a film), a compression problem with loading surfaces impenetrable to dislocations, and a tension problem involving shear band formation. In all the cases, the formulation in which eight-node elements with reduced integration and four-node elements with full integration are used respectively for displacement rates and the GND density rates gives reasonable solutions. In addition to the discussion on the choice of finite elements, detailed behavior in gradient-dependent solids, such as the accumulation of GND density and the distribution of backstress on each slip system, is investigated by utilizing the reliable computational results obtained.     

Size dependent response of large shell elements under in-plane tensile loading

Large-scale thin-walled structures with a low weight-to-stiffness ratio provide the means for cost and energy efficiency in structural design. However, the design of such structures for crash and impact resistance requires reliable FE simulations. Large shell elements are used in those simulations. Simulations require the knowledge of the true stress–strain response of the material until fracture initiation. Because of the size effects, local material relation determined with experiments is not applicable to large shell elements. Therefore, a numerical method is outlined to determine the effect of element size on the macroscopic response of large structural shell elements until fracture initiation. Macroscopic response is determined by introducing averaging unit into the numerical model over which volume averaged equivalent stress and plastic strain are evaluated. Three different stress states are considered in this investigation: uniaxial, plane strain and equi-biaxial tension. The results demonstrate that fracture strain is highly sensitive to size effects in uniaxial tension whereas in plane strain or equi-biaxial tension size effects are much weaker. In uniaxial and plane strain tension the fracture strain for large shell elements approaches the Swift diffuse necking condition.     

New spatial curved beam and cylindrical shell elements of gradient-deficient Absolute Nodal Coordinate Formulation

Based on previous studies, a new spatial curved slender-beam finite element and a new cylindrical shell finite element are proposed in the frame of gradient-deficient Absolute Nodal Coordinate Formulation (ANCF). The strain energy of the beam element is derived by using the definition of the Green?CLagrange strain tensor in continuum mechanics so that the assumption on small strain can be relaxed. By using the differential geometry and the continuum mechanics, the angle between two base vectors of a defined local coordinate frame of the cylindrical shell element is introduced into the strain energy formulations. Therefore, the new shell element can be used to model parallelogram shells. The analytical formulations of elastic forces and their Jacobian for the above two finite elements of gradient-deficient ANCF are also derived via the skills of tensor analysis. The generalized-alpha method is used to solve the huge set of system equations. Finally, four case studies including both static and dynamic problems are given to validate the proposed beam and cylindrical shell elements of gradient-deficient ANCF.     

FATIGUE GROWTH MODELING OF MIXED-MODE CRACK IN PLANE ELASTIC MEDIA

This paper presents an extension of a displacement discontinuity method with cracktip elements （a boundary element method） proposed by the author for fatigue crack growth analysis in plane elastic media under mixed-mode conditions. The boundary element method consists of the non-singular displacement discontinuity elements presented by Crouch and Starfield and the crack-tip displacement discontinuity elements due to the author. In the boundary element implementation the left or right crack-tip element is placed locally at the corresponding left or right crack tip on top of the non-singular displacement discontinuity elements that cover the entire crack surface and the other boundaries. Crack growth is simulated with an incremental crack extension analysis based on the maximum circumferential stress criterion. In the numerical simulation, for each increment of crack extension, remeshing of existing boundaries is not required because of an intrinsic feature of the numerical approach. Crack growth is modeled by adding new boundary elements on the incremental crack extension to the previous crack boundaries. At the same time, the element characteristics of some related elements are adjusted according to the manner in which the boundary element method is implemented. As an example, the fatigue growth process of cracks emanating from a circular hole in a plane elastic plate is simulated using the numerical simulation approach.     

Constructive symmetry in the stability problem for a cylindrical shell reinforced by stiffening rings under hydrostatic pressure

We use the solution of the problem under study which was earlier obtained by the author [1—3] and which is based on a decomposition of the reinforced shell into separate constructive elements (the ribs and the shell itself) and then on deriving the equilibrium equations and consistency conditions for their strains. Under the assumption that the shell precritical state is momentless, this is a sufficiently exact solution. Its drawback is the significant complexity of the computational algorithm. In the present paper, we show that the laboriousness of the algorithm can be reduced dramatically if the shell under study has elements of design symmetry (identical ribs, their uniform spacing, or both). In addition, we present dependencies determining the stiffening rib rigidity needed to ensure that the shell remains stable for a given critical value of the external hydrostatic pressure.     

Analysis of shells reinforced by massive stiffening ribs

The paper presents results of applying a heterogeneous mathematical model “elastic body–Timoshenko shell” to design shells with massive ribs. Numerical results are obtained for a cylindrical shell with ribs. They are compared with results obtained using the theory of elasticity and the theory of Timoshenko shells with piecewise-constant thickness Published in Prikladnaya Mekhanika, Vol. 44, No. 11, pp. 132–142, November 2008.     

Dynamic problems for and stress–strain state of inhomogeneous shell structures under stationary and nonstationary loads

This paper reviews studies and analyzes results on the effect of discrete ribs on the dynamic characteristics of rectangular plates and cylindrical shells. Use is made of the vibration equations derived from the classical theories of beams, plates, and shells. The effect of Pasternak’s elastic foundation on the critical velocities of a structurally orthotropic model of a ribbed cylindrical shell is determined. Nonstationary problems are solved for perforated and ribbed shells of revolution filled with a fluid or resting on an elastic foundation and subjected to moving or impulsive loads. Results from studies of the behavior of sandwich shell structures under impulsive loads of various types are presented     

A boundary element modeling of fatigue crack growth in a plane elastic plate

This paper presents an extension of a boundary element method to fatigue growth analysis of mixed-mode cracked plane elastic bodies. The method consists of the non-singular displacement discontinuity element presented by Crouch and Starfield and the crack-tip displacement discontinuity element due to the author. In the boundary element implementation the left or the right crack-tip element is placed locally at the corresponding left or right crack tip on top of non-singular displacement discontinuity elements that cover the entire crack surface and the other boundaries. Crack growth is simulated with an incremental crack extension analysis based on the modified maximum strain energy density criterion. In numerical simulation, for each increment of crack extension, remeshing of existing boundaries is not required because of an intrinsic feature of the boundary element method. Crack growth is simulated by adding new boundary elements on the incremental crack extension to the previous crack boundaries. At the same time, the element characters of some related elements are adjusted according to the manner in which the boundary element method is implemented. Some numerical results of fatigue growth in a plane elastic plate with a center-inclined crack under uniaxial cyclic loading are given.