Analysis of laminated shells of revolution with laminated stiffeners using a doubly curved quadrilateral finite element

A finite element analysis of laminated shells of revolution reinforced with laminated stifieners is described here-in. A doubly curved quadrilateral laminated anisotropic shell of revolution finite element of 48 d.o.f. is used in conjunction with two stiffener elements of 16 d.o.f. namely: (i) A laminated anisotropic parallel circle stiffener element (PCSE); (ii) A laminated anisotropic meridional stiffener element (MSE).These stifiener elements are formulated under line member assumptions as degenerate cases of the quadrilateral shell element to achieve compatibility all along the shell-stifiener junction lines. The solutions to the problem of a stiffened cantilever cylindrical shell are used to check the correctness of the present program while it's capability is shown through the prediction of the behavior of an eccentrically stiffened laminated hyperboloidal shell.     

金属加筋板压缩稳定性分析的随机缺陷法

为使金属加筋板稳定性分析更加真实可靠,在分析中引入随机的初始几何缺陷,采用一致缺陷法通过ANSYS对金属加筋板进行压缩稳定性有限元分析,总结一致缺陷法的优缺点,进而提出一种考虑加筋板初始几何缺陷的随机缺陷法并进行试验.结果表明:一致缺陷法对非线性变形分析有一定的引导作用,使非线性变形朝着特征值屈曲模态的方向发展;随机缺陷法将结构的初始缺陷看作是随机的,缺陷大小和分布无法预测,更能反映加筋板真实的工作性能.编写加筋板自动建模程序和随机缺陷自动分析程序,从而大大提高分析效率,使随机缺陷法用于设计成为可能.     

Modeling techniques for adina analysis of stiffened shell structures

The ADINA beam element is inadequate for transient analysis of eccentrically stiffened shell structures, particularly when the lateral stability of the stiffener is of concern. As an alternative to modeling stiffened shells with a large number of continuum or transition elements, a stiffener modeling technique based on the ADINA multi-point constraint option is presented. This technique leads to significant reductions in the number of elements and solution degrees of freedom needed for accurate stiffener modeling, yet allows effects of out-of-plane web distortion, longitudinal warping and torsion to be included in the analysis. Stiffeners with various cross section geometries and boundary conditions have been modeled and predicted response correlates well with experimental data. The approach is of practical significance for large stiffened shell problems, especially for nonlinear analysis.     

A finite element large displacement analysis of stiffened plates

A finite element analysis of the large deflection behaviour of stiffened plates using the isoparametric quadratic stiffened plate bending element is presented. The evaluation of fundamental equations of the stiffened plates is based on Mindlin's hypothesis. The large deflection equations are based on von Kármán's theory. The solution algmrithm for the assembled nonlinear equilibrium equations is based on the Newton-Raphson iteration technique. Numerical solutions are presented for rectangular plates and skew stiffened plates.     

Solid to shell element geometric transformation

The geometric transformation applied to three-dimensional solid elements producing the so-called degenerate shell element is reviewed. An alternative to generating the shell element directly is proposed. The solid element is integrated first, with appropriate modifications to the material matrix. Then the shell element is generated from this matrix in a manner resembling ordinary geometrical transformations. The net result is the same stiffness matrix with reduced effort and simpler coding.     

Finite element analysis of bimodulus composite stiffened thin shells of revolution

This paper is a sequel to the work published by the first and third authors[l] on stiffened laminated shells of revolution made of unimodular materials (materials having identical properties in tension and compression). A finite element analysis of laminated bimodulus composite thin shells of revolution, reinforced by laminated bimodulus composite stiffeners is reported herein. A 48 dot doubly curved quadrilateral laminated anisotropic shell of revolution finite element and it's two compatible 16 dof stiffener finite elements namely: (i) a laminated anisotropic parallel circle stiffener element (PCSE) and (ii) a laminated anisotropic meridional stiffener element (MSE) have been used iteratively.The constitutive relationship of each layer is assumed to depend on whether the fiberdirection strain is tensile or compressive. The true state of strain or stress is realized when the locations of the neutral surfaces in the shell and the stiffeners remain unaltered (to a specified accuracy) between two successive iterations. The solutions for static loading of a stiffened plate, a stiffened cylindrical shell. and a stiffened spherical shell, all made of bimodulus composite materials, have been presented.     

Analysis of laminated shells with laminated stiffeners using rectangular shell finite elements

A finite element analysis of laminated shells reinforced with laminated stiffeners is described in this paper. A rectangular laminated anisotropic shallow thin shell finite element of 48 d.o.f. is used in conjunction with a laminated anisotropic curved beam and shell stiffening finite element having 16 d.o.f. Compatibility between the shell and the stiffener is maintained all along their junction line. Some problems of symmetrically stiffened isotropic plates and shells have been solved to evaluate the performance of the present method. Behaviour of an eccentrically stiffened laminated cantilever cylindrical shell has been predicted to show the ability of the present program. General shells amenable to rectangular meshes can also be solved in a similar manner.     

Thin shell and surface crack finite elements for simulation of combined failure modes

In this study we present a new approach to analyse cracked shell structures subjected to large geometric changes. It is based on a combination of a rectangular assumed natural deviatoric strain thin shell finite element and an improved linespring finite element. Plasticity is accounted for using stress resultants. A power law hardening model is used for shell and linespring material. A co-rotational formulation is employed to represent nonlinear geometry effects. With this, one can carry out nonlinear fracture mechanics assessments in structures that show instabilities due buckling (local/global), ovalisation and large rigid body motion. By numerical examples it is shown how geometric instabilities and fracture compete as governing failure mode.     

Interactive-adaptive geometrically nonlinear analysis of shell structures

This paper presents an investigation of interactive-adaptive techniques for nonlinear finite element structural analysis. In particular, effective methods leading to reliable automated, finite element solutions of nonlinear shell problems are of primary interest here. This includes automated adaptive nonlinear solution procedures based on error estimation and adaptive step length control, reliable finite elements that account for finite deformations and finite rotations, three-dimensional finite element modeling, and an easy-to-use, easy-to-learn graphical user interface with three-dimensional graphics. A computational environment, which interactively couples a comprehensive geometric modeler, an automatic three-dimensional mesh generator and an advanced nonlinear finite element analysis program with real-time computer graphics and animation tools, is presented. Three examples illustrate the merit and potential of the approaches adopted here and confirm the feasibility of developing fully automated computer aided engineering environments.     

Flexural analysis of reinforced fibrous concrete members using the finite element method

A numerical procedure based on the finite element method is developed for the geometric and material nonlinear analysis of reinforced concrete members containing steel fibres and subjected to monotonic loads. The proposed procedure is capable of tracing the displacements, strains, stresses, crack propagation, and member end actions of these structures up to their ultimate load ranges. A frame element with a composite layer system is used to model the structure. An iterative scheme based on Newton-Raphson's method is employed for the nonlinear solution algorithm. The constitutive models of the nonlinear material behaviour are presented to take into account the nonlinear stress-strain relationships, cracking, crushing of concrete, debonding and pull-out of the steel fibres, and yielding of the reinforcement. The geometric nonlinearity due to the geometrical change of both the structure and its elements are also represented. The numerical solution of a number of reinforced fibrous concrete members are compared with published experimental test results and showed good agreement.     

Numerical methods for optimization of nonlinear shell structures

A numerical method for the optimal design of nonlinear shell structures is presented. The nonlinearity is only geometrical and the external load is assumed to be conservative. The nonlinear shell is analysed using standard nonlinear shell finite elements with the displacements and the rotation of the shell normals as independent analysis variables. Shell thicknesses and cross-sectional dimensions of beam stiffeners are used as design variables. The nonlinear optimization problem is solved using a Newton barrier method. The usefulness of the proposed method is demonstrated on shallow stiffened shell structures exhibiting significant nonlinear response.Presented at NATO ASI Optimization of Large Structural Systems, Berchtesgaden, Sept. 23 – Oct. 4, 1991     

Structural synthesis of frame reinforced,submersible, circular,cylindrical hulls

This paper describes a mathematical programming procedure for the automated optimal structural synthesis of frame stiffened, cylindrical shells. For a specified set of design parameters such as external pressure, shell radius and length and material properties, the method generates those values of the design variables that produce a minimum weight design. The skin, frame web and frame flange thicknesses and the flange width are treated as continuous variables. Frame spacing is considered a discrete variable. Constraint equations control local and general shell and frame instability and yield. Limits may be placed on the variable values, and certain geometric or space constraints can be applied. The mixed (continuous and discrete nonlinear programming problem is solved by a combination of a discrete ‘Golden Search’ for the optimal number of frames and the ‘Direct Search Design Algorithm’ which provides the optimum values of the continuous variables.     

Reinforcement layout and sizing optimization of composite submarine sail structures

A topology optimization approach that makes use of nonlinear design variable-to-sizing relationship is presented. A finite element (FE) model is used to describe the loaded structure, but unlike the microstructure approach, the decision is whether an element in the continuum should have maximum or minimum cross-sectional dimension while its material density and moduli are held constant. This approach is applied to reinforcement layout optimization of a very large and geometrically complex Composite Advanced Sail (CAS) structure under an asymmetric wave slap loading condition. A high-complexity model in the form of multilayered shell and a low-complexity model in the form of stiffened shell are developed for the layout optimization of the CAS and solved for minimum strain energy. The effects of constraints such as buckling instability on optimal placement of internal stiffeners are also explored. Based on the results of the layout optimization, a new FE model of the CAS is developed and optimized for minimum weight. Depending upon the degree of variability in skin thickness, the results show a weight saving of up to 19% over the original model.     

Coupled shell-fluid interaction problems with degenerate shell and three-dimensional fluid elements

Discrete methods for practical coupled three-dimensional fluid-structure interaction problems are developed. A C° explicitly integrated two-dimensional degenerate shell element and a three-dimensional fluid element are coupled to study shell dynamics, fluid transient and coupled shell-fluid interaction problems. The method of partitioning is used to integrate the fluid and shell meshes in a staggered fashion in an optimum manner. Effective explicit-implicit partitioning is shown to achieve high computational efficiency for this type of problem.     

Instability analysis of Skylab structure

A computer program for the linear and nonlinear analysis of shell structures (STAGS) is applied to the instability analysis of a complex stiffened structure subjected to complicated sets of distributed and concentrated loads. Results obtained from two-dimensional bifurcation and nonlinear collapse analyses are presented. The nonlinear analysis includes the effects of an imperfection in a shell stiffened by heavy longerons. Several problems associated with the analysis of very large eigenvalue problems are discussed (one case involved a model with 20,910 degrees-of-freedom). These include the use of the appropriate finite-difference formulation to ensure convergence in a desired direction (approaching the asymptotic value either from above or from below) and the use of variable grid spacing to induce buckling in one part of the structure or the other. A technique of finding higher eigenvalues by removing the prestress at the point of bifurcation is described.     

Bifurcation and collapse analysis of stringer and ring-stringer stiffened cylindrical shells with cutouts

This paper presents results for cylindrical shell configurations using the STAGS computer program. Discontinuities have been imposed upon the shell's skin by incorporating symmetrical cutout openings. In addition, the surface is stiffened with both stringer and ring-stringer arrangements.The cutout problem has been shown to be highly nonlinear for smooth surface shells, but the author has found that bifurcation and collapse loads are close when one is considering stiffened skin configurations. In order to arrive at this conclusion, it was necessary to evaluate the following:—comparison between smeared and discrete stiffener theory for linear solutions—numerical finite difference convergence as directed toward buckling determination—collapse load results with the various skin stiffeners.This paper also includes a linear bifurcation study relating to stiffening effects around cutout areas present within stringer and ring-stringer shell surfaces. Comparisons have been made between a variety of geometric positions considering cutout frame and thickened skin additions. The investigation points toward an optimum positioning.     

Finite element analysis of stiffened plates

A finite element method is presented in which the constraint between stiffener and member is imposed by means of Lagrange multipliers. This is performed on the functional level, forming augmented variational principles. In order to simplify the initial development and implementation of the proposed method, two-dimensional stiffened beam finite elements are developed. Several such elements are formulated, each showing monotonic convergence in numerical tests. In the development of stiffened plate finite elements, the bending and membrane behaviors are treated seperately. For each, the stiffness matrix of a standard plate element is modified to account for an added beam element (representing the stiffener) and additional terms imposing the constraint between the two. The resulting stiffened plate element was implemented in the SAPIV finite element code. Exact solutions are not known for rib-reinforced plated structures, but results of numerical tests converge monotonically to a value in the vicinity of an approximate “smeared” series solution.     

Large displacement extension of consistent shell element for static and dynamic analysis

The superior performance of the consistent shell element in the small deflection range has encouraged the authors to extend the formulation to large displacement static and dynamic analyses. The nonlinear extension is based on a total Lagrangian approach. A detailed derivation of the non-linear extension is based on a total Lagrangian approach. A detailed derivation of the non-linear stiffness matrix and the unbalanced load vector for the consistent shell element is presented in this study. Meanwhile, a simplified method for coding the nonlinear formulation is provided by relating the components for the nonlinear B-matrices to those of the linear B-matrix. The consistent mass matrix for the shell element is also derived and then incorporated with the stiffness matrix to perform large displacement dynamic and free vibration analyses of shell structures. Newmark's method is used for time integration and the Newton-Raphson method is employed for iterating within each increment until equilibrium is achieved. Numerical testing of the nonlinear model through static and dynamic analyses of different plate and shell problems indicates excellent performance of the consistent shell element in the nonlinear range.     

Geometrically nonlinear analysis of cylindrical shells using surface-parallel quadratic elements

A moderately thick cylindrical shell isoparametric element that is capable of accurately modeling cylindrically curved geometry, while also incorporating appropriate through-thickness kinematic relations is developed. The analysis accounts for fully nonlinear kinematic relations so that stable equilibrium paths in the advanced nonlinear regime can be accurately predicted. The present nonlinear finite element solution methodology is based on the hypothesis of linear displacement distribution through thickness (LDT) and the total Lagrangian formulation. A curvilinear side 16-node element with eight nodes on each of the top and bottom surfaces of a cylindrical shell has been implemented to model the transverse shear/normal deformation behavior represented by the LDT. The BFGS iterative scheme is used to solve the resulting nonlinear equations. A thin-shallow clamped cylindrical panel is investigated to test the convergence of the present element, and also to compare the special case of the present solution based on the KNSA (von Karman strain approximation) with those computed using the available faceted elements, discrete Kirchhoff constraint theory (DKT) and classical shallow shell finite elements, spanning the entire computed equilibrium path.     

A nine-node assumed-strain finite element for composite plates and shells

A new finite element for modeling fiber-reinforced composite plates and shells is developed and its performance for static linear problems is evaluated. The element is a nine-node degenerate solid shell element based on a modified Hellinger-Reissner principle with independent inplane and transverse shear strains. Several numerical examples are solved and the solutions are compared with other available finite solutions and with classical lamination theory. The results show that the present element yields accurate solutions for the test problems presented. Convergence characteristics are good, and the solution is relatively insensitive in element distortion. The element is also shown to be free of locking even for thin laminates.