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.     

Doubly-curved variable-thickness isoparametric heterogeneous finite element

This paper describes an element streamlined for the analysis of doubly-curved, variable-thickness structural components and illustrates its effective application to vibration and static problems. The element is isoparametric, doubly-curved, thin-shell and triangular with variable thickness and accounts for anisotropic, inhomogeneous elastic material behavior. The element has six nodes (three corner and three mid-side) with five degrees-of-freedom (DOF) per node—three translations and two rotations. Quadratic isoparametric interpolation polynomials are used to express the element geometry and displacement variables in terms of corresponding nodal variables.     

SESAM-69—A general purpose finite element method program

The multilevel superelement method in combination with extensive data generators materialized in the program system SESAM-69 introduce a new dimension to the concept of the Finite Element Method (FEM).The paper describes the superelement method and the program system SESAM-69 in brief terms. However, the major part contains some of the program analytics in connection with this method. The multilevel superelement method is an extension of the better known substructure technique, or reduction procedure. The method applies to both statics and dynamics.     

Mixed isoparametric finite element models of laminated composite shells

Mixed shear-flexible isoparametric elements are presented for the stress and free vibration analysis of laminated composite shallow shells. Both triangular and quadrilateral elements are considered. The “generalized” element stiffness, consistent mass, and consistent load coefficients are obtained by using a modified form of the Hellinger-Reissner mixed variational principle. Group-theoretic techniques are used in conjunction with computerized symbolic integration to obtain analytic expressions for the stiffness, mass and load coefficients. A procedure is outlined for efficiently handling the resulting system of algebraic equations.The accuracy of the mixed isoparametric elements developed is demonstrated by means of numerical examples, and their advantages over commonly used displacement elements are discussed.     

Evaluation of integrals for a ten-node isoparametric tetrahedral finite element

The use of isoparametric finite elemts in solving three-dimensional problems typically requires the numerical evaluation of a large number of integrals over individual element domains. The evaluation of these integrals by numerical quadrature, which is the traditional approach, can be computationally expensive. For certain problems the present study provides a more efficient method for evaluation of the needed integrals. For these problems some or all of the desired integrals can be evaluated as linear combinations of basic integrals whose integrands are either (i) products of shape (interpolation) functions or (ii) a derivative of a shape function times a product of one or more shape functions. Basic integrals of these two types (when written in terms of local coordinate systems) have integrands which are polynomial both in the variables of integration and in the nodal coordinates and, thus, can be expressed as linear combinations (with rational number coefficients) of a set of polynomial functions of the nodal coordinates. Group theoretic techniques can be employed to select appropriate sets of polynomial functions for use in these expansions and to reduce substantially the number of basic integrals which need to be explicitly evaluated.

The details for the approach have been worked out for a ten-node isoparametric tetrahedral element through the use of MACSYMA, a computer system for algebraic manipulation. The symmetry group for this element has order 24. The basic integrals of types (i) and (ii) are expressed as linear combinations of 20 and 26 terms, respectively. The special case of a straight-edged tetrahedral element with mid-edge nodes is also discussed.     

A high order isoparametric finite element method for the computation of waveguide modes

We have studied the approximation of optical waveguide eigenvalues by a high order isoparametric vector finite element method. Isoparametric mappings are used for the approximation of domains with curved boundaries or curved material interfaces. Eigenvalue convergence for curved elements is investigated. Numerical results verify the predicted order of convergence and show the remarkable accuracy of the method.     

Determining invertible two and three dimensional quadratic isoparametric finite element transformations

This paper presents an algorithm determining the invertibility of any planar, triangular quadratic isoparametric finite element transformation. Extensions of the algorithm to three-dimensional isoparametric finite element transformations yield conditions which guarantee invertibility of 10-node tetrahedra and 8-node bricks.     

An isoparametric finite element with decreased sensitivity to midside node location

A modified isoparametric finite element formulation is developed which is insensitive to midside node placement. An eight-node plane element is developed using the modified approach. Numerical results are presented for both the standard serendipity and modified isoparametric eight-node elements. These results demonstrate that decreased sensitivity to midside node placement occur when the modified formulation is used.     

A simple contour plotting program for finite element output

An algorithm to produce piecewise linear contour plots for finite element output is described. Several examples are shown to demonstrate the application of the algorithm.     

A finite element method for investigating general elastic multi-structures

A finite element method is proposed for investigating the general elastic multi-structure problem, where displacements on bodies, longitudinal displacements on plates, longitudinal displacements and rotational angles on rods are discretized using conforming linear elements, transverse displacements on plates and rods are discretized respectively using TRUNC elements and Hermite elements of third order, and the discrete generalized displacement fields in individual elastic members are coupled together by some feasible interface conditions. The unique solvability of the method is verified by the Lax–Milgram lemma after deriving generalized Korn’s inequalities in some nonconforming element spaces on elastic multi-structures. The quasi-optimal error estimate in the energy norm is also established. Some numerical results are presented at the end.     

A conoidal shell analysis by modified isoparametric element

The quadratic isoparametric element is modified for applications in thin shell analysis. Four extra nonconforming displacement modes are added to transverse displacement then, later, they are eliminated through static condensation. A conoidal shell under uniform pressure is analyzed using the new element and the results compared with previous works.     

A general finite element model for shells of arbitrary geometry

A finite element formulation is developed for the large displacement analysis of arbitrary shells. Formulation is based on a convected coordinate system and a tensorial approach is followed. The strain-displacement relationships used do not reflect the Kirchhoff hypothesis and Love's approximations. Isoparametric interpolation is used for the discretization of the problem, and the number of nodal points is variable. The numerical examples include the buckling analysis of cylindrical shells as well as two problems to test the convergence and accuracy of the algorithm.     

A computer program for perspective projection of three-dimensional finite element models

The theoretical basis of a computer program prepared for plotting the perspectives of 3-D finite element models with consideration of the hidden line removal technique is presented. The algorithm is successfully implemented in a FORTRAN 77 program. The validity of the algorithm and its implementation is verified through use of two typical examples. The program may be used in input data error correction and output data reduction of finite element programs.     

A three-dimensional finite element program to predict ultimate fracture failure load

A finite element computer program using an eight-noded three-dimensional isoparametric finite element is developed to predict the initiation and propagation of fracture, load-displacement history and failure load in elastoplastic structural systems subjected to monotonically increasing loads. Isotropie material is considered. The program is based on small deformation theory and uses an incremental loading technique to load the structure. The approach uses two types of piecewise linear approximations for the non-linear portion of the actual uniaxial stress-strain curve for the material: (i) the tangent modulus concept and (ii) the secant modulus concept. Either the St. Venant or von Mises yielding criteria can be used to predict yielding or fracture. Three different methods of calculating element principal stresses/strains are incorporated to apply the yield criterion. The energy at fracture is redistributed by using the ‘zero modulus unload-reload scheme’. Two different problems are solved using the developed program to demonstrate its capabilities and accuracy: (i) a center cracked panel and (ii) a tubular T-connection. The results obtained by the finite element analyses compare well with the available results from experimental tests on similar specimens.     

A general three-dimensional L-section beam finite element for elastoplastic large deformation analysis

In this paper, the development of a general three-dimensional L-section beam finite element for elastoplastic large deformation analysis is presented. We propose the generalized interpolation scheme for the isoparametric formulation of three-dimensional beam finite elements and the numerical procedure is developed for elastoplastic large deformation analysis. The formulation is general and effective for other thin-walled section beam finite elements. To show the validity of the formulation proposed, a 2-node three-dimensional L-section beam finite element is implemented in an analysis code. As numerical examples, we first perform elastic small and large deformation analyses of a cantilever beam structure subjected to various tip loadings, and elastoplastic large deformation analysis of the same structure under reversed cyclic tip loading. We then analyze the failures of simply supported beam structures of different lengths and slenderness ratios under elastoplastic large deformation. The same problems are solved using refined shell finite element models of the structures. The numerical results of the L-section beam finite element developed here are compared with the solutions obtained using shell finite element analyses. We also discuss the numerical solutions in detail.     

Cubic isoparametric rolling/traveling finite elements

In this paper, the development and formulation of a new cubic isoparametric rolling/travelling finite element is described. The element can be used to simulate the dyanamic response of steadily rolling/traveling viscoelastic structures without the necessity of numerical time integration of the governing equations. Due to its higher order shape function, the element can more accurately simulate both the inertia and viscoelastic effects associated with rolling/traveling structures than currently available lower order moving elements. To illustrate the capabilities of the new cubic element, comparisons with exact and lower order generated results are presented.     

NASTRAN—a finite element program for structural analysis

Nastran has been designed for NASA to handle large problems with any degrees of freedom. The user can either instruct the executive system to perform the operations he wishes or he can make use of one of twelve rigid formats, each of which performs a particular analysis. Lloyd's Register are at present evaluating Nastran. Container ships and supertankers pose new structural problems whose solution may require 10 000–15 000 degrees of freedom.