A smoothed finite element method for shell analysis

A four-node quadrilateral shell element with smoothed membrane-bending based on Mindlin-Reissner theory is proposed. The element is a combination of a plate bending and membrane element. It is based on mixed interpolation where the bending and membrane stiffness matrices are calculated on the boundaries of the smoothing cells while the shear terms are approximated by independent interpolation functions in natural coordinates. The proposed element is robust, computationally inexpensive and free of locking. Since the integration is done on the element boundaries for the bending and membrane terms, the element is more accurate than the MITC4 element for distorted meshes. This will be demonstrated for several numerical examples.     

Fluid–shell structure interaction analysis by coupled particle and finite element method

This paper presents a coupled particle and finite element method for fluid–shell structure interaction analysis. The Moving Particle Semi-Implicit (MPS) method is used to analyze fluid flow and the MITC4 shell element is used in the FEM analysis of the structure. This paper considers partitioned coupling between the fluid and structural solvers. In order to satisfy compatibility in the employed partitioned coupling scheme, the Neumann–Dirichlet condition is applied to both the fluid and the structure. A symplectic time integration scheme is used to preserve energy when analyzing the shell structure. If the frequencies of the shell analysis are much higher than those of the MPS fluid solver, its time integration scheme is sub-cycled. When the presented coupling scheme was applied to simulate the sloshing phenomenon in an elastic thin shell structure, fluid fragmentation and large structural deformations were observed.     

Nonlinear finite element analysis of shell structures using the semi-loof element

The Semi-Loof Shell element originally developed by Irons [2] for linear elastic analysis of thin shell structures is formulated to include large deflection and plastic deformation effects. In this paper the details of the finite element formulation of the problem using total Lagrangian coordinate systems are presented and different element matrices are given. For plastic materials following the Prandtl-Reuss flow rule with isotropic strain hardening a multi-layer approach using a subincremental technique is employed. Numerical results on the performance of the element for a variety of applications are presented. These computer studies include complete load-deflection curves into the post-buckling range and comparisons are made with other existing results. Current experience with the element indicates that it is a reliable and competitive element for nonlinear analysis of shells of general geometry.     

Generalized stochastic finite element method in elastic stability problems

The main issue of this paper is the stability analysis of elastic systems with random parameters using the Generalized Stochastic Finite Element Method. The Taylor expansion with random coefficients of nth order is used to express all random functions and to determine up to fourth order probabilistic moments of the critical force or critical pressure. The response function method assists to determine higher order partial derivatives of the structural response instead of the Direct Differentiation Method employed widely before. This approach is examined on the classical Euler problem, 2D and 3D steel frames as well as in addition to the cylindrical shell with some geometrical parameters defined as the Gaussian variables. The comparison of the GSFEM versus the Monte-Carlo simulation on the Euler problem proves the probabilistic convergence of this new technique.     

A conical shell finite element

In the analysis of rocket and missiles structures one frequently encounters cylindrical and cornica' shells. A simple finite element which fits the above configuration is obviously a conical shell finite element. In this paper stiffness matrix for a conical shell finite element is derived using Novozhilov's strain-displacement relations for a conical shell. Numerical integration is carried out to ge. the stiffness matrix. The element has 28 degrees-of-freedom and is nonconforming. An eigenvalue analysis of the stiffness matrix showed that it contains all the rigid body modes (six in this case) adequately, which is one of the convergence criteria. An advantage of this element is that a cylindrical shell, an annular segment flat plate, a rectangular flat plate elements can easily be obtained as degenerate cases. The effectiveness of this element is shown through a variety of numerical examples pertaining to annular plate, cylindrical shell and conical shell problems. Comparison of the present solution is made with the existing ones wherever possible. The comparison shows that the present element is superior in some respects to the existing elements     

Geometrically nonlinear analysis of shell structures using a flat triangular shell finite element

Summary This paper presents a state of the art review on geometrically nonlinear analysis of shell structures that is limited to the co-rotational approach and to flat triangular shell finite elements. These shell elements are built up from flat triangular membranes and plates. We propose an element comprised of the constant strain triangle (CST) membrane element and the discrete Kirchhoff (DKT) plate element and describe its formulation while stressing two main issues: the derivation of the geometric stiffness matrix and the isolation of the rigid body motion from the total deformations. We further use it to solve a broad class of problems from the literature to validate its use.     

基于强度折减法的边坡稳定性非线性有限元分析

利用强度折减法,根据基于摩尔库仑屈服准则的广义米塞斯屈服准则(D-P准则),结合MSC Marc对某多介质边坡和含非贯通结构面岩质边坡稳定性进行非线性有限元分析,分别比较用4种不同D-P准则计算的结果.比较结果表明:利用MSC Marc程序中的理想弹塑性材料,结合线性摩尔库仑模型,通过对材料强度折减至极限平衡的临界状态,可以计算出边坡的安全因数,并较精确地计算出边坡失稳的危险面.该方法能分析各种复杂的边坡,可以为工程治理提供参考.     

A geometrically nonlinear shell finite element for tire vibration analysis

An axisymmetric finite element is developed which includes such features as orthotropic material properties, doubly curved geometry, and both the first and second order nonlinear stiffness terms. This element can be used to predict the equilibrium state of an axisymmetric shell structure with geometrically nonlinear large displacements. Small amplitude vibration analysis can then be performed based on this equilibrium state. The nonlinear path is predicted by using the self-correcting incremental procedure and any point on the path can be checked by using the Newton-Raphson iterative scheme. The present formulation and solution procedure are evaluated by analyzing a series of examples with results compared with alternative known solutions. Examples include: free vibration of an isotropic cylindrical shell, a conical frustum, and an orthotropic cylindrical shell; buckling of a cylindrical shell; large deflection of a clamped disk, a spherical cap, and a steel belted radial tire. The final example is a free vibration analysis of the inflated tire and the natural frequencies obtained compared well with published experimental data.     

Dynamic stability analysis of a composite material planar mechanism by the finite element method

Vibration analysis has become one of the most important considerations in the design of machines for high-speed operation. Dynamic stability may occur in high-speed flexible mechanisms. The use of composite materials which possess high strength to weight and high stiffness to weight ratios may improve these problems. The Euler beam theory is used to study the dynamic stability of a planar four-bar mechanism made from composite material. The operation condition is assumed to be at a steady dynamic state. The Ritz finite element procedure is used to solve the dynamic stability problem. The advantages of using composite materials are demonstrated.     

A nonlinear finite element analysis of an ice-strengthened ship shell structure

Finite element method is used to study the nonlinear behaviour of an ice-strengthened ship shell structure. The main object is the plastification and collapse of a frame. The plastic limit load for this frame is determined using the calculated load-deflection curve. The results of the finite element analysis are compared with well-known formulas of plastic design and also with experimental results. The finite element program used in the analysis is ADINA.     

On the stability of the finite element immersed boundary method

The immersed boundary (IB) method is a mathematical formulation for fluid–structure interaction problems, where immersed incompressible visco-elastic bodies or boundaries interact with an incompressible fluid.The original numerical scheme associated to the IB method requires a smoothed approximation of the Dirac delta distribution to link the moving Lagrangian domain with the fixed Eulerian one.We present a stability analysis of the finite element immersed boundary method, where the Dirac delta distribution is treated variationally, in a generalized visco-elastic framework and for two different time-stepping schemes.     

A simple isoparametric three-node shell finite element

A three-node isoparametric shell finite element including membrane and bending effects is proposed. The element is based on the degenerated solid approach and uses an assumed strain method to avoid shear locking. An intermediate convected covariant frame is used in order to construct the modified shear strain interpolation matrix. Validation tests show that shear locking is avoided and that a reduced integration procedure can be used without any loss of accuracy which is useful for the numerical efficiency.     

An error estimation method in finite element structural analysis

In the paper a new interpretation of the finite element approach is described and illustrated numerically. The conventional shape functions of the displacement—and stress—type finite element models are treated as constraints imposed on the continuous medium considered. This enables a consistent error estimation analysis based on a concept of so-called reaction forces and deformation incompatibilities.     

On the validity of an approximation available in the finite element shell analysis

A simplified displacement method is proposed for the finite element shell analysis. This method requires two kinds of shape functions in the evaluation of the membrane and bending stiffness of the shell to curtail the computational processes of the usual displacement method. Mathematical and numerical studies are also made to establish the validity of the approach.     

Application of a new stress finite element to analysis of shell structures

A new stress finite element for analysis of shell structures of arbitrary geometry and loading has been introduced in Ref. [1]. The purpose of the present paper is to demonstrate the versatility of the proposed element with respect to all kinds of shell structures.     

A finite element analysis of an axisymmetrically loaded orthotropic shell of revolution

The objective of this study was to develop a finite element matrix method of analysis for symmetrically loaded orthotropic shells of revolution using closed form elasticity solutions for the element. A computer program for structural analysis was developed based on this method.

The program was used to analyze orthotropic cylindrical shells with edge loads, orthotropic spherical shells with edge loads, and pressurized ellipsoidal shells.

For the ellipsoidal shells, the ratio of the major to minor axis (a/b) varied from 0.2 to 1.8. The orthotropic materials used had ratios of Young's modulus in the meridional direction to Young's modulus in a direction tangent to a parallel circle (E₁/E₂) that ranged from 0.2 to 1.8.

For the structures and orthotropic materials studied, it was found that the edge effect, as signified by the meridional moment, was affected by the Young's moduli ratio E₁/E₂, the radius of curvature R₂ in the plane containing a normal to the shell surface and a tangent to a parallel circle, and Poisson's ratio v₂, the latter being more prominent for large E₁/E₂ values. The range of the E₁/E₂ ratio caused the meridional edge moment to double, increasing as the E₁/E₂ ratios increased from 0.2 to 1.8, for pressurized ellipsoidal shells. The meridional edge moment more than doubled as the ellipsoidal axes ratio, a/b, ranged from 0.2 to 1.8.     

On finite element large displacement and elastic-plastic dynamic analysis of shell structures

Finite element procedures for nonlinear dynamic analysis of shell structures are presented and assessed. Geometric and material nonlinear conditions are considered. Some results are presented that demonstrate current applicabilities of finite element procedures to the nonlinear dynamic analysis of two-dimensional shell problems. The nonlinear response of a shallow cap, an impulsively loaded cylindrical shell and a complete spherical shell is predicted. In the analyses the effects of various finite element modeling characteristics are investigated. Finally, solutions of the static and dynamic large displacement elastic-plastic analysis of a complete spherical shell subjected to external pressure are reported. The effect of initial imperfections on the static and dynamic buckling behavior of this shell is presented and discussed.     

A finite element method for localized failure analysis

A method is proposed which aims at enhancing the performance of general classes of elements in problems involving strain localization. The method exploits information concerning the process of localization which is readily available at the element level. A bifurcation analysis is used to determine the geometry of the localized deformation modes. When the onset of localization is detected, suitably defined shape functions are added to the element interpolation which closely reproduce the localized modes. The extra degrees of freedom representing the amplitudes of these modes are eliminated by static condensation. The proposed methodology can be applied to 2-D and 3-D problems involving arbitrary rate-independent material behavior. Numerical examples demonstrate the ability of the method to resolve the geometry of localized failure modes to the highest resolution allowed by the mesh.