充液压电阻尼圆柱壳的有限元建模

基于Mindlin板理论、压电理论、粘弹性理论和理想流体方程，对充液圆柱壳主动约束阻尼结构在流固耦合条件下的建模进行了研究。利用拉格朗日方法得到结构的动力学方程，利用GHM方法描述粘弹性阻尼的本构关系，结合流体方程建立主动约束阻尼结构在流固耦合条件下的动力学方程。建立从压电材料的电压到流固耦合边界下的圆柱壳结构振动的频响函数，利用实验结果对理论计算加以验证，结果表明该建模方法是可行的。     

A solid‐like shell element allowing for arbitrary delaminations

In this contribution a new finite element is presented for the simulation of delamination growth in thin‐layered composite structures. The element is based on a solid‐like shell element: a volume element that can be used for very thin applications due to a higher‐order displacement field in the thickness direction. The delamination crack can occur at arbitrary locations and is incorporated in the element as a jump in the displacement field by using the partition of unity property of finite element shape functions. The kinematics of the element as well as the finite element formulation are described. The performance of the element is demonstrated by means of two examples. Copyright © 2003 John Wiley & Sons, Ltd.     

A nonlinear composite shell element with continuous interlaminar shear stresses

A numerical model for layered composite structures based on a geometrical nonlinear shell theory is presented. The kinematic is based on a multi-director theory, thus the in-plane displacements of each layer are described by independent director vectors. Using the isoparametric apporach a finite element formulation for quadrilaterals is developed. Continuity of the interlaminar shear stresses is obtained within the nonlinear solution process. Several examples are presented to illustrate the performance of the developed numerical model.List of symbols reference surface - convected coordinates of the shell middle surface - ⁱ coordinate in thickness direction - ⁱ h thickness of layer i - X_o position vector of the reference surface - ⁱX_o position vector of midsurface of layer i - t _k orthonormal basis system in the reference configuration - ⁱ a _k orthonormal basis system of layer i - ⁱW axial vector - R_o orthonormal tensor in the reference configuration - ⁱ R orthonormal tensor of layer i - ⁱ Cauchy stress tensor - ⁱ P First Piola-Kirchhoff stress tensor - ⁱ q vector of interlaminar stresses - ⁱ n, ⁱ m vector of stress resultants and stress couple resultants - v _x components of the normal vector of boundary - ⁱ N, ⁱ Q, ⁱ M stress resultants and stress couple resultants of First Piola-Kirchhoff tensor - stress resultants and stress couple resultants of Second Piola-Kirchhoff tensor - ⁱ , ⁱ , ⁱ strains of layer i - _K transformation matrix - u_o displacement vector of layer 1 - ⁱ local rotational degrees of freedom of layer i     

Mixed-mode delamination growth of laminar composites by using three-dimensional finite element modeling

ABSTRACT Delamination is one of the most frequent failure modes in laminated composites. Its importance is crucial, because a delamination can occur in the interior of a panel without any noticeable damage on the surface, drastically reducing its strength and stiffness. A study has to be made on critical dimensions of delaminations and their shape, through the calculation of the strain energy release rate (SERR), G. This study was performed numerically, for a given geometry, with varying loads and shapes of delamination, in pure and mixed‐mode propagation. All numerical values were obtained with three‐dimensional finite element (FE) analyses from a commercial package. The use of three‐dimensional analyses in simple geometries helps establish the basis for the more complex ones, and the correspondence with the usual analytical or numerical bi‐dimensional plane‐strain analysis. The conclusions were (a) G is not constant along the crack tip, even for mode I propagation and straight crack tip; (b) the mean value of G obtained from a three‐dimensional analysis equals the value obtained in bi‐dimensional plane‐strain analysis; (c) in mixed‐mode propagation, the method exhibits a good correlation with experimental results and (d) the shape and mode partitioning of the SERR depend not only on the loading, but also on the shape of the crack front.     

A shell element for the prediction of residual load-carrying capacities due to delamination

This paper deals with layered plates and shells subjected to static loading. The kinematic assumptions are extended by a jump function in dependence of a damage parameter. Additionally, an intermediate layer is arranged at any position of the laminate. This allows numerical simulation of onset and growth of delaminations. The equations of the boundary value problem include besides the equilibrium in terms of stress resultants, the local equilibrium in terms of stresses, the geometric field equations, the constitutive equations, and a constraint which enforces the correct shape of a superposed displacement field through the thickness as well as boundary conditions. The weak form of the boundary value problem and the associated finite element formulation for quadrilaterals is derived. The developed shell element possesses the usual 5 or 6 degrees of freedom at the nodes. This is an essential feature since standard geometrical boundary conditions can be applied and the elements are applicable to shell intersection problems. With the developed model, residual load-carrying capacities of layered shells due to delamination failure are computed.     

Finite element analysis of elastic contact problems using differential displacements

A technique of differential displacements is presented whereby problems involving elastic contact are solved by the finite element method. The technique is applied to axisymmetric situations in which statically indeterminate conditions occur and is shown to provide a means for resolving these conditions in terms of contact stresses. Three typical engineering problems are analysed to demonstrate the technique in cases where body forces, thermal gradients and external applied forces are acting.     

Finite element simulation of delamination growth in composite materials using LS-DYNA

In this paper, a modified adaptive cohesive element is presented. The new elements are developed and implemented in LS-DYNA, as a user defined material subroutine (UMAT), to stabilize the finite element simulations of delamination propagation in composite laminates under transverse loads. In this model, a pre-softening zone is proposed ahead of the existing softening zone. In this pre-softening zone, the initial stiffness and the interface strength are gradually decreased. The onset displacement corresponding to the onset damage is not changed in the proposed model. In addition, the critical energy release rate of the materials is kept constant. Moreover, the constitutive equation of the new cohesive model is developed to be dependent on the opening velocity of the displacement jump. The traction based model includes a cohesive zone viscosity parameter (η) to vary the degree of rate dependence and to adjust the maximum traction. The numerical simulation results of DCB in Mode-I is presented to illustrate the validity of the new model. It is shown that the proposed model brings stable simulations, overcoming the numerical instability and can be widely used in quasi-static, dynamic and impact problems.     

Finite element analysis of 3-ply laminated conical shell for flutter

The results of the finite element analysis of 3-ply laminated conical shells with light core for linear panel flutter are presented and certain advantages of such shells discussed.     

Finite element analysis of interface delamination and buckling in thin film systems by wedge indentation

A finite element method is used to study the interface delamination and buckling of thin film systems subject to microwedge indentation. In the formulation, the interface adjoining the thin film and substrate is assumed to be the only site where cracking may occur. Both the thin film and the substrate are taken to be ductile materials with finite deformation. A traction-separation law, with two major parameters: interface strength and interface energy, is introduced to simulate the adhesive and failure behaviors of the interface between the film and the substrate. The effects of the interface adhesive properties and the thickness of the thin film on the onset and growth of interface delamination and the film buckling are investigated.     

Finite element procedures for parametric resonance phenomena of arbitrary elastic shell structures

A purely numerical method for the treatment of instability problems of parametric resonance is presented. The proposed way of solution, which is applicable to all types of structures, is based on the finite element discretization of an incremental variational principle. After the derivation of the theoretical background linear and quadratic eigenvalue problems for the critical excitation-frequencies of undamped and damped systems are presented and numerical procedures for the computation of the instability charts are established. Finally the efficiency of the developed algorithms is demonstrated by means of several shell responses.     

A generalized layerwise finite element for multi-layer damping treatments

This paper presents a 4-node facet type quadrangular shell finite element, based on a layerwise theory, developed for dynamic modelling of laminated structures with viscoelastic damping layers. The bending stiffness of the facet shell element is based on the Reissner–Mindlin assumptions and the plate theory is enriched with a shear locking protection adopting the MITC approach. The membrane component is corrected by using incompatible quadratic modes and the drilling degrees of freedom are introduced through a fictitious stiffness stabilization matrix. Linear static tests, using several pathological tests, showed good and convergent results. Dynamic analysis evaluation is provided by using two eigenproblems with exact analytical solution, as well as a conical sandwich shell with a closed-form analytical solution and a semi-analytical ring finite element solution. The applicability of the proposed finite element to viscoelastic core sandwich plates is assessed through experimental validation.     

Finite element modeling of the filament winding process

A finite element model of the wet filament winding process was developed. In particular, a general purpose software for finite element analysis was used to calculate the fiber volume fraction under different process conditions. Several unique user defined subroutines were developed to modify the commercial code for this specific application, and the numerical result was compared with experimental data for validation. In order to predict the radial distribution of the fiber volume fraction within a wet wound cylinder, three unique user defined subroutines were incorporated into the commercial finite element code: a fiber consolidation/compaction model, a thermochemical model of the resin and a resin mixing model. The fiber consolidation model describes the influence of the external radial compaction pressure of a new layer as it is wound onto the surface of existing layers. The thermochemical model includes both the cure kinetics and viscosity of the resin. This model analyzes the composite properties and tracks the viscosity of the resin, which is a function of the degree of cure of the resin. The resin mixing model describes the mixing of “old” and “new” resin as plies are compacted. Validations were made by comparing image analysis data of fiber volume fraction in each ply for filament wound cylinders with the FEM results. The good agreement of these comparisons demonstrated that the FEM approach has can predict fiber volume fraction over a range of winding conditions. This approach, then, is an invaluable tool for predicting the effects of winding parameters on cylinder structural quality.     

An assumed strain triangular solid shell element with bubble function displacements for analysis of plates and shells

Bubble function displacements are used in conjunction with the assumed strain formulation to construct efficient triangular solid shell elements tailored for shell analysis. Two versions of 36‐DOF triangular elements are presented with different bubble function displacements and the corresponding assumed strain fields. In the first version the bubble function displacement is independent of the thickness while in the second version the bubble function varies linearly in the thickness direction. The assumed strain fields are carefully selected to alleviate locking effect. The first version models curved shells with flat triangular elements. The second version is effective in alleviating the membrane locking and thus allows more accurate modelling of curved shells. Various numerical examples demonstrate the validity and effectiveness of the present assumed strain formulation elements with the bubble function displacements. Copyright © 2001 John Wiley & Sons, Ltd.     

Finite deformation formulation of a shell element for problems of sheet metal forming

An elastic-plastic thin shell finite element suitable for problems of finite deformation in sheet metal forming is formulated. Hill's yield criterion for sheet materials of normal anisotropy is applied. A nonlinear shell theory in a form of an incremental variational principle and a quasi-conforming element technique are employed in the Lagrangian formulation. The shell element fulfills the inter-element C ¹ continuity condition in a variational sense and has a sufficient rank to allow finite stretching, rotation and bending of the shell element. The accuracy and efficiency of the finite element formulation are illustrated by numerical examples.     

Finite element interface models for the delamination analysis of laminated composites: mechanical and computational issues

The finite element analysis of delamination in laminated composites is addressed using interface elements and an interface damage law. The principles of linear elastic fracture mechanics are indirectly used by equating, in the case of single‐mode delamination, the area underneath the traction/relative displacement curve to the critical energy release rate of the mode under examination. For mixed‐mode delamination an interaction model is used which can fulfil various fracture criteria proposed in the literature. It is then shown that the model can be recast in the framework of a more general damage mechanics theory. Numerical results are presented for the analyses of a double cantilever beam specimen and for a problem involving multiple delamination for which comparisons are made with experimental results. Issues related with the numerical solution of the non‐linear problem of the delamination are discussed, such as the influence of the interface strength on the convergence properties and the final results, the optimal choice of the iterative matrix in the predictor and the number of integration points in the interface elements. Copyright © 2001 John Wiley & Sons, Ltd.     

Finite element procedures for the nonlinear dynamic stability analysis of arbitrary shell structures

The objective is the development of numerical algorithms for the dynamic stability analysis of strongly nonlinear shell structures subjected, in particular, to parametric excitations. The finite-element discretization is achieved by displacement models of high accuracy. The basis for the stability analysis is Ljapunow's first approximation equation obtained from a finite-rotation shell theory by a variational method. The operator formulation used for this purpose shows the mathematical requirements imposed on consistent formulations. In close connection with Floquet's theory, a semi-analytical criterion is finally given for the stability analysis of parametric instability phenomena. The numerical results presented demonstrate the efficiency of the numerical algorithms.     

Finite element representation and pressure stiffness in shell stability analysis

In the light of recent contributions by Batoz¹ and Hibbitt,² two aspects of finite element formulations for shell stability analysis are examined. The first is the consistency of the shell strain-displacement equations employed; the second is the proper representation of ‘follower forces’—pressures that are always normal to the deforming surface. Numerical studies of an arch indicate that improper representation of either of these factors can have a significant effect on predicted buckling loads. Numerical studies of an arch indicate that improper representation of either of these factors can have a significant effect on predicted bukling loads.