ON THE STABILITY ANALYSIS OF PLATES AND SHELLS USING A QUADRILATERAL,16-DEGREES OF FREEDOM PLAT SHELL ELEMENT DKQ16

The linear buckling problems of plates and shells were analysed using a recently developped quadrilateral,16-degrees of freedom flat shell element (called DKQ16).The geometrical stiffness matrix was established.Comparison of the numerical results for several typical problems shows that the DKQ16 element has a very good precision for the linear buckling problems of plates and shells.

A Smoothed Finite Element Method for the Static and Free Vibration Analysis of Shells

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.

THE CONSTRUCTION OF WAVELET-BASED TRUNCATED CONICAL SHELL ELEMENT USING B-SPLINE WAVELET ON THE INTERVAL

Based on B-spline wavelet on the interval （BSWI）, two classes of truncated conical shell elements were constructed to solve axisymmetric problems, i.e. BSWI thin truncated conical shell element and BSWI moderately thick truncated conical shell element with independent slopedeformation interpolation. In the construction of wavelet-based element, instead of traditional polynomial interpolation, the scaling functions of BSWI were employed to form the shape functions through the constructed elemental transformation matrix, and then construct BSWI element via the variational principle. Unlike the process of direct wavelets adding in the wavelet Galerkin method, the elemental displacement field represented by the coefficients of wavelets expansion was transformed into edges and internal modes via the constructed transformation matrix. BSWI element combines the accuracy of B-spline function approximation and various wavelet-based elements for structural analysis. Some static and dynamic numerical examples of conical shells were studied to demonstrate the present element with higher efficiency and precision than the traditional element.

A FINITE ELEMENT ANALYSIS OF THE FLANGE EARRINGS OF STRONG ANISOTROPIC SHEET METALS IN DEEP-DRAWING PROCESSES

Flange earrings of strong anisotropic sheet metals in deep-drawing process are numerically analyzed by the elastic-plastic large deformation finite element formulation based on a discrete Kirchhoff triangle plate shell element model. A Barlat-Lian anisotropic yield function and a quasi-flow corner theory are used in the present formulation. The numerical results are compared with the experimental ones of cylindrical cup drawing process. The focus of the present researches is on the numerical analysis and the constraining scheme of the flange earring of circular sheets with strong anisotropy in square cup drawing process.

LOCKING-FREE DEGENERATED ISOPARAMETRIC SHELL ELEMENT

An 8-noded locking-free degenerated isoparametric shell element is presented. A revised interpolation for shear strain terms was constructed in natural co-ordinate system such that all necessary modes (translation, rotation and constant curvature) are preserved, which can be used to eliminate shear locking. A revised interpolation for membrane strains was produced in the local Cartesian co-ordinate system to overcome membrane locking behavior. The new 8-noded element has the proper rank, with the requisite number of zero eigenvalues each associated with a rigid mode. The element does not exhibit membrane or shear locking for large span-thickness ratio. The element does not form element mechanisms or extra spurious zero energy modes. Therefore, it can be used for both thin and thick shells.

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.

Numerical Simulation of Continuous Tension Leveling Process of Thin Strip Steel and Its Application

Cold-rolled thin strip steel of high flatness quality undergoes multistage deformation during tension leveling. Thus, the parameters of set-up and manipulating are more difficult. With the aid of FE code MSC. MARC, the tension leveling process of thin strip steel was numerically simulated. Concentrating on the influence of the roll intermeshes in 2# anti-cambering on the distribution and magnitude of residual stresses in leveled strip steel, several experiments were clone with the tension leveler based on the results from the simulation. It was found from the simulation that the magnitude of longitudinal residual stresses in the cross-section of the leveled strip steel regularly presents obvious interdependence with the roll intermeshes in 2# anti-cambering. In addition, there is a steady zone as the longitudinal residual stresses of the surface layers in leveled strip steel vary with the roll intermeshes of 2# anticambering, which is of importance in the manipulation of tension levelers. It was also found that the distribution of strains and stresses across the width of strip steel is uneven during leveling or after removing the tension loaded upon the strip, from which it was found that 3D simulation could not be replaced by 2D analysis because 2D analysis in this case cannot represent the physical behavior of strip steel deformation during tension leveling.

Modeling stationary and moving cracks in shells by X-FEM with CB shell elements

The continuum-based(CB)shell theory is combined with the extended finite element method(X-FEM)in this paper to model crack propagation in shells under static and dynamic situations.Both jump function and asymptotic crack tip solution are adopted for describing the discontinuity and singularity of the crack in shells.Level set method(LSM)is used to represent the crack surface and define the enriched shape functions.Stress intensity factors(SIFs)are calculated by the displacement interpolation technique to prove the capability of the method and the maximum strain is applied for the fracture criterion.Also,an efficient integration scheme for the CB shell element with cracks is proposed.

Reinforcement by polyurethane to stiffness of air-supported fabric formwork for concrete shell construction

By spraying concrete on inner surface,air-supported fabric structures can be used as formwork to construct reinforced concrete shell structures.The fabric formwork has the finished form of concrete structure.Large deviation from the desired shape of concrete shells still remains as central problem due to dead weight of concrete and less stiffness of fabric formwork.Polyurethane can be used not only as a bonding layer between fabrics and concrete but also as an additional stiffening layer.However,there is little research on mechanical behaviors of the polyurethane shell structure.This paper presents experimental studies on an inflated fabric model with and without polyurethane,including relief pressure tests,vertical loading tests and horizontal loading tests.Experimental results show that the additional polyurethane layer can significantly enhance the stiffness of the fabric formwork.Compared with the experiment,a numerical model using shell layered finite elements has a good prediction.The reinforcement by polyurethane to improve stiffness of air-supported fabric formwork is expected to be considered in the design and construction of the concrete shell,especially dealing with the advance of shape-control.

Nonlinear dynamic response analysis of supercavitating vehicles

A finite element model for the supercavitating underwater vehicle was developed by employing 16-node shell elements of relative degrees of freedom.The nonlinear structural dynamic response was performed by introducing the updated Lagrangian formulation.The numerical results indicate that there exists a critical thickness for the supercavitating plain shell for the considered velocity of the vehicle.The structure fails more easily because of instability with the thickness less than the critical value,while the structure maintains dynamic stability with the thickness greater than the critical value.As the velocity of the vehicle increases,the critical thickness for the plain shell increases accordingly.For the considered structural configuration,the critical thicknesses of plain shells are 5 and 7 mm for the velocities of 300 and 400 m/s,respectively.The structural stability is enhanced by using the stiffened configuration.With the shell configuration of nine ring stiffeners,the maximal displacement and von Mises stress of the supercavitating structure decrease by 25% and 17% for the velocity of 300 m/s,respectively.Compared with ring stiffeners,longitudinal stiffeners are more significant to improve structural dynamic performance and decrease the critical value of thickness of the shell for the supercavitating vehicle.

SPRINGBACK SIMULATION AND ANALYSIS OF STRONG ANISOTROPIC SHEET METALS IN U-CHANNEL BENDING PROCESS

The springback phenomenon of strong anisotropic sheet metals with U-channel bending as well as deep-drawing is numerically studied in detail by using Updating Lagrange FEM based on virtual work-rate principle, Kirchhoff shell element models and the Barlat-Lian planar anisotropic yield function. Simulation results are compared with a benchamark test. Very good agreement is obtained between numerical and test results. The focus of the present study is on the numerical simulation of the springback characteristics of the strong anisotropic sheet metals after unloading. The effects of the planar anisotropy coefficients and yield function exponent in the B-L yield function on the springback characteristics are discussed in detail. Some conclusions are given.

Effects of Thermo-Mechanical Loads on Aeroelastic Instabilities of Metallic and Composite Panels

Panel flutter phenomena can be strongly affected by thermal loads,and so a refined aeroelastic model is presented.Higher-order shell theories are used as structural models.The aerodynamic forces are described using the Piston theory.The temperature is considered uniform over the thickness of the panel.The aero-thermo-elastic model is derived in the framework of the Carrera unified formulation(CUF),therefore the matrices are expressed in a compact form using the″fundamental nuclei″.Composite and sandwich structures are considered and different boundary conditions are taken into account.The effects of the thermal load on the aeroelastic behavior are investigated.

NUMERICAL STUDY ON FLANGING AND SPRINGBACK OF STAMPED THICK METAL PLATE

A quasi-three-dimensional shell element model, which can beeffectively used to simulate the flanging and spring-backdeformation, is introduced into the independently developed CAEsoftware, KMAS, In this model, a double surface contact algorithm,which allows the gap between punch and die to change, and a spring-back treatment scheme based on finite element meshing are described.And then the flanging and spring-back deformations of the retractor'skickstand of a railcar made of stamped thick metal plate arenumerically simulated. The simulation results of flanging deformationare compared with those of international commercial software,PAM-STAMP, and experimental ones. Finally, a predicting scheme ofspring-back quantily for this problem is given.

Static shape control of a flat shell structure

The eight-node and forty-DOF piezoelectric shell element were applied to shape control of a flat shell structure. By the direct and converse effects, a distributed piezoelectric sensor layer was used to monitor the shape deformation and a distributed actuator layer was used to suppresse the deflection. A finite element model was for static response of laminated shell with piezoelectric sensors/actuators was derived. The model was verified by calculating piezoelectric polymeric PVDF bimorph beam. The results are in good agreement with those obtained by theoretical analysis of Tzou and Hwang . A case study of the static shape control of a flat shell structure is presented.

FLANGE EARING AND ITS CONTROL ON DEEP-DRAWING OF ANISOTROPY CIRCULAR SHEETS

The Hill's quadric anisotropy yield function and the Barlat-Lian anisotropy yield func- tion describing well anisotropy sheet metal with stronger texture are introduced into a quadric-flow cor- ner constitutive theory of elastic-plastic finite deformation suitable for deformation localization analy- sis.And then,the elastic-plastic large deformation finite element formulation based on the virtual power principle and the discrete Kirchhoff shell element model including the yield functions and the constitutive theory are established.The focus of the present research is on the numerical simulation of the flange earing of the deep-drawing of anisotropy circular sheets,based on the investigated results, the.schemes for controlling the flange earing are proposed.

Numerically Simulating the Sandwich Plate System Structures

Sandwich plate systems (SPS) are advanced materials that have begun to receive extensive attention in naval architecture and ocean engineering.At present, according to the rules of classification societies, a mixture of shell and solid elements are required to simulate an SPS.Based on the principle of stiffness decomposition, a new numerical simulation method for shell elements was proposed.In accordance with the principle of stiffness decomposition, the total stiffness can be decomposed into the bending stiffness and shear stiffness.Displacement and stress response related to bending stiffness was calculated with the laminated shell element.Displacement and stress response due to shear was calculated by use of a computational code write by FORTRAN language.Then the total displacement and stress response for the SPS was obtained by adding together these two parts of total displacement and stress.Finally, a rectangular SPS plate and a double-bottom structure were used for a simulation.The results show that the deflection simulated by the elements proposed in the paper is larger than the same simulated by solid elements and the analytical solution according to Hoff theory and approximate to the same simulated by the mixture of shell-solid elements, and the stress simulated by the elements proposed in the paper is approximate to the other simulating methods.So compared with calculations based on a mixture of shell and solid elements, the numerical simulation method given in the paper is more efficient and easier to do.

Numerical and Experimental Investigation of an Elliptical Paraboloid Shell Model

For practical engineering purpose, a new flat shell element baptized （ACM_Q4SBE1） is presented in this paper. The formulated element can be used for the analysis of thin shell structures; no matter how the geometrical shape might be. Tests on standard problems have been examined. Since, the analysis of thin shell structures has generally been purely carried out on a theoretical basis; it is of importance to present some experimental results of an elliptical paraboloid under uniformly distributed load pressure. The results obtained from both numerical and experimental work are presented.

One-piece coal mine mobile refuge chamber with safety structure and less sealing risk based on FEA

In order to reduce the risk of sealing and improve the structural strength for a coal mine mobile refuge chamber,a new type of one-piece model was designed.Mechanical and mathematical calculation performed an important role.Calculated according to statics and relevant contents,the structure had the same total volume as the traditional segmented structure,but had shorter length,wider width and greater height.Those prevented the structure from stress or deformation failure.Some reinforcing ribs with enough moments of inertia were welded in the external shell.Because of the one-piece structure,this refuge chamber reduced the risk of sealing which was a serious problem of segmented structure.Impact load with 300 ms duration and0.6 MPa over-pressure was settled.Explicit nonlinear dynamic analysis program was used to simulate the response of the refuge chamber.The maximum stress and the maximum displacement were obtained.The refuge chamber including blast airtight doors could meet the rigidity requirement.Weak parts of the chamber were the front and back end shell where bigger displacement values occurred than others.Thus,the calculation indicated that the refuge chamber could meet structural safety requirements.Based on the numerical analysis,suggestions were put forward for further resistance ability improvement.Only large inclined shaft with larger wellhead was suitable for this one-piece coal mine mobile refuge chamber.

NUMERICAL ANALYSIS OF BIFURCATION BUCKLING FOR ROTATIONALLY PERIODIC STRUCTURES UNDER ROTATIONALLY PERIODIC LOADS

By considering the characteristics of deformation of rotationally periodic structures under rotationally periodic loads, the periodic structure is divided into some identical substructures in this study. The degrees-of-freedom (DOFs) of joint nodes between the neighboring substructures are classified as master and slave ones. The stress and strain conditions of the whole structure are obtained by solving the elastic static equations for only one substructure by introducing the displacement constraints between master and slave DOFs. The complex constraint method is used to get the bifurcation buckling load and mode for the whole rotationally periodic structure by solving the eigenvalue problem for only one substructure without introducing any additional approximation. The finite element (FE) formulation of shell element of relative degrees of freedom (SERDF) in the buckling analysis is derived. Different measures of tackling internal degrees of freedom for different kinds of buckling problems and different stages of numerical analysis are presented. Some numerical examples are given to illustrate the high efficiency and validity of this method.

A novel enriched CB shell element method for simulating arbitrary crack growth in pipes

In this work, a novel numerical method is developed for simulating arbitrary crack growth in pipes with the idea of enriched shape functions which can represent the discontinuity independent of the mesh. The concept of the enriched shape functions is introduced into the continuum-based (CB) shell element. Due to the advantage of CB shell element, the shell thickness varia- tion and surface connection can be concerned during the deformation. The stress intensity factors of the crack in the CB shell element are calculated by using the 'equivalent domain integral' method for 3D arbitrary non-planar crack. The maximum en- ergy release rate is used as a propagation criterion. This method is proved able to capture arbitrary crack growth path in pipes which is independent of the element mesh. Numerical examples of different fracture patterns in pipes are presented here.