Shell Finite Element Method Research Articles

Three-dimensional multiscale simulation on fracture behaviors of cylindrical shells subjected to inner pressure and surface laser irradiation

Multiscale numerical simulation has important advantages in analyzing the partial fracture problems of shell structures subjected to the coupled thermo-mechanical effects. The multiscale time–space model of a cylindrical shell subjected to inner pressure and surface laser irradiation by coupling the three-dimensional discrete element method (DEM) and the shell finite element method was established. By simulating the crack-bifurcation extending behaviors of the aluminum alloy cylindrical shell and comparing the fracture behaviors and the calculation time by the multiscale time–space model with those by the multiscale space model of the overlapping element/node, the multiscale time–space model not only satisfies the requirement of simulation accuracy, but also enhances the calculation efficiency greatly under the condition of stable simulation. The multiscale time–space model was applied to the simulations in the fracture behaviors of the aluminum alloy and the 30CrMnSiA steel cylindrical shells under four modes of action. The failure modes of cylindrical shells under different modes of action are directly related to the radius of the laser spot, the power density of the laser, and the extensibility of material. At the same time, the damage evolution process of the cylindrical shells under four modes of action was analyzed through the crack ratio in the mesoscopic DEM elements. The multiscale time–space model provides a reliable analytical way to the complex partial fracture mechanical problems of large-scale cylindrical shell structures subjected to inner pressure and surface laser irradiation. PACS. 02.70.Dh, 02.70.Ns, 42.62.Cf, 46.50.+a, 61.82.Bg, 62.20.mm, 07.05.Tp, 83.60.Uv

Influence of bending resistance on the dynamics of a spherical capsule in shear flow

The objective of the paper is to study the effect of wall bending resistance on the motion of an initially spherical capsule freely suspended in shear flow. We consider a capsule with a given thickness made of a three-dimensional homogeneous elastic material. A numerical method is used to model the fluid-structure interactions coupling a boundary integral method for the fluids with a shell finite element method for the capsule envelope. For a given wall material, the capsule deformability strongly decreases when the wall bending resistance increases. But, if one expresses the same results as a function of the two-dimensional mechanical properties of the mid-surface, which is how the capsule wall is modeled in the thin-shell model, the capsule deformed shape is identical to the one predicted for a capsule devoid of bending resistance. The bending rigidity is found to have a negligible influence on the overall deformation of an initially spherical capsule, which therefore depends only on the elastic stretching of the mid-surface. Still, the bending resistance of the wall must be accounted for to model the buckling phenomenon, which is observed locally at low flow strength. We show that the wrinkle wavelength is only a function of the wall bending resistance and provide the correlation law. Such results can then be used to infer values of the bending modulus and wall thickness from experiments on spherical capsules in simple shear flow.

Dynamics of a Spherical Capsule in a Planar Hyperbolic flow: Influence of bending Resistance

We consider an initially spherical capsule freely suspended in a planar hyperbolic flow and study the influence of the wall bending resistance on the capsule dynamics. The capsule wall is assumed to be made of a three-dimensional homogeneous elastic material. The fluid-structure interaction between the capsule and the external flow is modeled numerically by coupling a boundary integral method with a shell finite element method. It is found that, for given three-dimensional wall mechanical properties, the capsule deformability is drastically reduced as the bending resistance is increased. But, if one expresses the same results as a function of the two-dimensional mechanical properties of the mid-surface, which is how the capsule wall is modeled in the thin-shell model, the capsule deformed shape is identical to the one predicted for a capsule devoid of bending resistance. The bending rigidity is found to have a negligible influence on the shape and deformation: the capsule main deformation mode is thus solely a function of the elastic stretching of the mid-surface. The wall bending resistance still plays a role locally in the regions where buckling occurs. Its influence is studied in the low flow strength regime, for which wrinkling of the wall is observed to persist at steady state. We show that the wrinkle wavelength only depends on the bending number, which compares the relative importance of bending and shearing phenomena, and provide the correlation law. This result is interesting as it allows bending resistance to be estimated from experiments on capsules in a planar hyperbolic flow at low flow strength.

Thermomechanical-Phase Transformation Simulation of High-Strength Steel in Hot Stamping

The thermomechanical-phase transformation coupled relationship of high-strength steel has important significance in forming the mechanism and numerical simulation of hot stamping. In this study a new numerical simulation module of hot stamping is proposed, which considers thermomechanical-transformation multifield coupled nonlinear and large deformation analysis. In terms of the general shell finite element and 3D tetrahedral finite element analysis methods related to temperature, a coupled heat transmission model for contact interfaces between blank and tools is proposed. Meanwhile, during the hot stamping process, the phase transformation latent heat is introduced into the analysis of temperature field. Next the thermomechanical-transformation coupled constitutive models of the hot stamping are considered. Static explicit finite element formulae are adopted and implemented to perform the full numerical simulations of the hot stamping process. The hot stamping process of typical U-shaped and B-pillar steel is simulated using the KMAS software, and a strong agreement comparison between temperature, equivalent stress, and fraction of martensite simulation and experimental results indicates the validity and efficiency of the hot stamping multifield coupled constitutive models and numerical simulation software KMAS. The temperature simulated results also provide the basic guide for the optimization designs of cooling channels in tools.

Ritz Approach for Buckling Prediction of Cracked-Stiffened Structures

The objective of the current paper is to present a Ritz-type solution for the buckling analysis of cracked-orthogonally stiffened panels. A cracked-orthogonally stiffened panel is defined as a rectangular plate with a crack and that has stiffeners that are parallel to one of its sides. Such structures are typically used as stiffened wing skins and fuselage skins in aerospace engineering. The behavior prediction of a cracked-stiffened panel using the Ritz approach is considered in the paper. In the Ritz-type solution, we use the local trigonometric trial functions to define the displacement function of the crack-stiffened panel, which is discretized into several elements based on the crack location and stiffener location. The interface continuity conditions for cracked thin-walled structures are derived and investigated in detail; the interface conditions are used to condense the global eigenvalue problem by eliminating redundant Ritz coefficients. Examples are presented to illustrate the effectiveness of the current model for buckling analysis. Buckling results from the current model are found to agree well with those obtained using a shell finite element method.

Global buckling of thin-walled simply supported columns: Numerical studies

In this paper numerical studies on global buckling of thin-walled members are presented. Various methods are used including classical analytical solutions, the semi-analytical finite strip method, the generalized beam theory, shell finite element method and the recently derived shell-model-based analytical formulae. Critical forces are calculated for flexural, pure torsional and flexural–torsional buckling of columns with various thin-walled cross-sections, the results are compared to each other and conclusions are drawn. As it is proved by the studies, the various methods yield similar results in many cases, but significant differences sometimes occur. The differences in the critical forces are due to various factors, these factors are fully explored and illustrated. Guidance is also given on how to minimize the differences between the various methods.

Parametric formulae for axial stiffness of CHS X-joints subjected to brace axial tension

Recent research has shown that circular hollow section (CHS) joints may exhibit non-rigid behavior under axial load or bending. The non-rigid behavior significantly affects the mechanical performance of structures. This paper is concerned with the parametric formulae for predicting axial stiffness of CHS X-joints while braces are in tension. The factors influencing the axial stiffness of CHS X-joints under brace axial tension are investigated, including the joint geometric parameters, the axial force of the chord, and bending moments of braces in two directions, etc. Effects of various parameters on axial stiffness of CHS X-joints are examined by systematic single-parameter nonlinear analysis using shell finite element methods. The analysis is implemented in a finite element code, ANSYS. The observed trends form the basis of the formulae for calculating the joint axial stiffness under brace axial tension by multivariate regression technique. In order to simplify the formulae, two non-dimensional variables are introduced. The proposed formulae can be used to calculate the joint axial stiffness in the design of single-layer steel tubular structures.

Buckling mode identification of thin-walled members by using cFSM base functions

The objective of this paper is to demonstrate an approximate method whereby eigen buckling modes from a shell finite element method (FEM) analysis of a thin-walled member can be quantified in terms of the fundamental buckling classes, namely, global, distortional, local, or other. The buckling classes are defined using the mechanical definitions employed in the constrained finite strip method ( cFSM). The cFSM base vectors are used to approximate an arbitrary FEM buckling mode. The resulting identification and its associated error is investigated, including dependency on FEM discretization, the number of cFSM functions considered, boundary conditions, and loading. The long-term goal of the work is to provide a generalized method for identification of local, distortional, and global buckling modes for arbitrary thin-walled members modeled in general purpose finite element codes.

Analysis and calculation of axial stiffness of tubular X-joints under compression on braces

This paper introduces the influence factors of axial stiffness of tubular X-joints. The analysis model of tubular joints using plate and shell finite element method is also made. Systematic single-parameter analysis of tubular X-joints is performed using Ansys program. The influences of those factors, including ratio of brace diameter to chord diameter (β), ratio of chord diameter to twice chord thickness (γ), ratio of brace wall thickness to that of chord (τ), brace-to-chord intersection angle (θ), and chord stress ratio, ratio of another brace diameter to chord diameter, in-plane and out-of-plane moment of braces, etc., on stiffness of tubular X-joints are analyzed. Two non-dimensional parameters—joint axial stiffness factor η N and axial force capacity factor ω N are proposed, and the relationship curve of the two factors is determined. Computational formulas of tubular X-joint axial stiffness are obtained by multi-element regression technology. The formulas can be used in design and analysis of steel tubular structures.

Damping Characteristics of Cylindrical Laminates with Viscoelastic Layer Considering Temperature- and Frequency-Dependence

The vibration and damping characteristics of the cylindrical hybrid panels with viscoelastic layers were investigated by using a full layerwise shell finite element method which can consider temperature and frequency dependent material properties. The present layerwise shell theory can accurately represent the zig-zag in-plane and out-of-plane displacements of multilayered hybrid structures and can fully consider the transverse shear and normal strains and the perfect cylindrical geometry. The remarkable differences of the frequency response functions of cylindrical hybrid panels including constrained layer damping and co-cured sandwiched models were observed. Present results show that the damping mechanics of hybrid panels with viscoelastic layers may be greatly affected by their temperature and frequency dependent material properties and that the present full layerwise theory can be used to accurately predict the vibration and damping characteristics of hybrid shells with viscoelastic layers.

Analysis of thin-walled frames considering joint flexibilities

TAnalytical models are developed for static and dynamic analysis of thin-walled frames representing the automotive side structures. The model is based on one-dimensional beam theory that considers joint flexibility to compute stiffness and frequency response of the whole frame structure. The computed out-of-plane displacements under static and impact loading are in good agreement with those obtained from the shell finite element method. Using the validated analytical model, the influence of joint flexibility on the elastic response of the side structure is studied.

A new skeletal model for fabric drapes

Fabric drapes are typical large displacement, large rotation and small strain problems. Compared with continuum shell finite element methods, methods that skeletonize the fabric sheet into a set of interconnected nodes appear to be more popular in drape problems with extensive wrinkles. These skeletal methods may resort to particle mechanics and formulate the elastic energy or the equations of motion in terms of the node-to-node distance and the angles between the straight lines joining adjacent nodes. Alternatively, beam elements can be employed to skeletonize the fabric sheet at the expense of using rotational in addition to translational nodal DOFs. In this paper, a new skeletal model based on the small strain and curvature assumptions is devised. In contrast to most, if not all, skeletal models for fabric drape simulation, all the stretching, shearing and bending energies in the model are simple polynomials of the grid-point␣displacement. Fabric drape problems with extensive wrinkles are examined. The presence of sharp fold, seam and cut in the undeformed fabric sheet as well as fabric-to-solid contact are considered. The predicted appearances are pleasant and conform to real life observations.

An equivalent-boundary method for the shell analysis of buried pipelines under fault movement

A new shell finite element method (FEM) model with an equivalent boundary is presented for estimating the response of a buried pipeline under large fault movement. The length of affected pipeline under fault movement is usually too long for a shell-mode calculation because of the limitation of memory and time of computers. In this study, only the pipeline segment near fault is modeled with plastic shell elements to study the local buckling and the large section deformation in pipe. The material property of pipe segment far away from the fault is considered as elastic, and nonlinear spring elements at equivalent boundaries are obtained and applied to two ends of shell model. Compared with the fixed-boundary shell model, the shell model with an equivalent boundary proposed by the study can remarkably reduce the needed memory and calculating time.

A co‐rotational grid‐based model for fabric drapes

AbstractFabric drapes are typical large displacement, large rotation and small strain problems. Compared to conventional geometric non‐linear shell analyses, computational fabric drape analysis is particularly challenging due to the extremely weak bending rigidities of fabrics. Compared to continuum shell finite element methods, grid‐ or particle‐based methods appear to be more successful in high drapeability problems. The latter methods often resort to simple particle mechanics and formulate the elastic energy in terms of the inter‐particle distances and trigonometrical functions of the angles between the straight lines joining adjacent particles. In this paper, the co‐rotational approach and commonly employed assumptions for small strain problems in finite element analysis will be adopted to formulate the elastic energy. It will be seen that the internal force vector and the stiffness matrix are considerably simpler than other grid‐based models, yet the sparsity of the tangential stiffness matrix remains unchanged. A number of examples are considered and the predicted results are promising. Copyright © 2003 John Wiley & Sons, Ltd.

Stresses in ellipsoidal pressure vessel heads with noncentral nozzle

The objective of this paper is further investigation of the shell intersection problem. The shell theory and finite element method are used for stress analysis of nozzle connections in ellipsoidal heads of the pressure vessels. Ellipsoidal heads having attached nozzles considerably displaced from the head axis are mainly considered. The features of the numerical procedure, structural modeling of nozzle-head shell intersections and SAIS special-purpose computer program are discussed. The results of stress analysis and parametric study of an ellipsoidal vessel head with a noncentral nozzle under internal pressure loading are presented.

Hydroelastic Effects on Propeller Blades in Steady Flow

The stress distribution and the deflection of blades of various screw propellers in steady flow are computed by the thick shell finite element (FE) method in combination with the surface panel method. A new general method is proposed to estimate the bicubic surface parameters of the deformed blade and to resolve the non-linear relation between the FE displacement distribution and the geometrical parameters of blade profiles on cylindrical sections. The characteristics of the surface flow on rigid and deflected blades are computed applying an approximation by Taylor's series expansion and minimization of the perturbation velocities. A modified hydroelastic interaction procedure is employed to obtain correspondence between the deformed blade form and the generated pressure distribution.For a few propellers with different blade outline, the flow and the deformation patterns are shown and two main trends of opposite changes of the hydrodynamic characteristics are emphasized. In each case we investigated the influences of the variation of designed spanwise thickness distribution on the performance of the propeller.

Stress Analysis of Shell Intersections With Torus Transition Under Internal Pressure Loading

Thin shell theory and finite element method were used to investigate shell intersections with torus transition. The developed special-purpose computer program SAIS is employed for elastic stress analysis of the shell intersections. Comparison of calculated results with experimental data are presented. The parametric study of models for the radial nozzle connections in shells under internal pressure loading was performed. The results are presented in graphical form. Nondimensional geometric parameters are considered to analyze the effects of changing these parameters on stress ratios in the shell intersections.

Stress analysis of nonradial cylindrical shell intersections subjected to external loading

Thin shell theory and finite element methods were used to investigate nonradial intersections of cylindrical shells subjected to external loadings. A parametric study of the nonradial intersections using a developed special-purpose computer program SAIS was performed. The presented numerical results show the effects of changing geometric and angular parameters on the stress ratios in shell intersection under external loadings on the branch shell.

Dynamic response of cantilever cylindrical shells with discontinuity in thickness subjected to axisymmetric load

Cylindrical shells with discontinuity in the thickness and subjected to harmonic axisymmetric load are analyzed for a clamped-free end condition. The loadings considered are uniform internal pressure and circular ring load at the tip. The semi-analytical finite element method is used for the analysis. A thin shell finite element method is used for the analysis. A thin shell finite element with four degrees of freedom per node and two nodes per element is used. Three shell models are analyzed for possible reduction of maximum displacement and maximum stress by choosing the discontinuity at different locations. Numerical results are presented for the first three modes and for various step-ratios in the thickness. The weight of the shell is kept constant for various step-ratios. It is shown that the maximum displacement and maximum stress decreases for certain types of thickness variations.

Stress Analysis of Ellipsoidal Shell With Nozzle Under Internal Pressure Loading

This paper presents the numerical procedure for the stress analysis of the intersecting shells consisting of an ellipsoidal shell and nozzle. Thin shell theory and finite element method are used. The developed special-purpose computer program SAIS is employed for elastic stress analysis of the model joints of the ellipsoidal shell with nozzle. The parametric study of the joints under internal pressure loading was performed. The results are presented in graphical form. Nondimensional geometric parameters are considered to analyze the effects of changing these parameters on the maximum effective stresses in the shells.