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1.
A new resultant force formulation of 8-node solid element is presented for the linear and nonlinear analysis of thin-walled structures. The global, local and natural coordinate systems were used to accurately model the shell geometry. The assumed natural strain methods with plane stress concept were implemented to remove the various locking problems appearing in thin plates and shells. The correct warping behavior in the very thin twisted beam test was obtained by using an improved Jacobian transformation matrix. The 2 × 2 Gauss integration scheme was used for the calculation of the element stiffness matrix. From the computational viewpoint, the present solid element is very efficient for a large scale of nonlinear modeling. A lot of numerical tests were carried out for the validation of the present 8-node solid-shell element and the results are in good agreement with references.An erratum to this article can be found at 相似文献
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3.
Large strain elastic-plastic theory and nonlinear finite element analysis based on metric transformation tensors 总被引:1,自引:0,他引:1
M. Brünig 《Computational Mechanics》1999,24(3):187-196
The present paper is concerned with an efficient framework for a nonlinear finite element procedure for the rate-independent
finite strain analysis of solids undergoing large elastic-plastic deformations. The formulation relies on the introduction
of a mixed-variant metric transformation tensor which will be multiplicatively decomposed into a plastic and an elastic part.
This leads to the definition of an appropriate logarithmic strain measure whose rate is shown to be additively decomposed
into elastic and plastic strain rate tensors. The mixed-variant logarithmic elastic strain tensor provides a basis for the
definition of a local isotropic hyperelastic stress response in the elastic-plastic solid. Additionally, the plastic material
behavior is assumed to be governed by a generalized J
2 yield criterion and rate-independent isochoric plastic strain rates are computed using an associated flow rule. On the numerical
side, the computation of the logarithmic strain tensors is based on 1st and higher order Padé approximations. Estimates of
the stress and strain histories are obtained via a highly stable and accurate explicit scalar integration procedure which
employs a plastic predictor followed by an elastic corrector step. The development of a consistent elastic-plastic tangent
operator as well as its implementation into a nonlinear finite element program will also be discussed. Finally, the numerical
solution of finite strain elastic-plastic problems is presented to demonstrate the efficiency of the algorithm.
Received: 17 May 1998 相似文献
4.
Wanji Chen Y. K. Cheung 《International journal for numerical methods in engineering》1992,35(9):1871-1889
In this paper a new hybrid variational principle with independent variables of strain, stress and displacement and with a weaker constraint condition of interelement continuity is proposed. Based on this functional, a general formulation of a refined hybrid isoparametric element method has been established by the orthogonal approach. The present formulation is a rational approach to be adopted for deriving high-performance three-dimensional hybrid isoparametric elements even up to the higher-order 20-node element. Several numerical examples are presented to show that the present elements RGH8(8-node) and RGH20(20-node) have high accuracy, excellent computational efficiency and less sensitivity to mesh distortion. 相似文献
5.
R. L. Spilker S. M. Maskeri E. Kania 《International journal for numerical methods in engineering》1981,17(10):1469-1496
Formulation and applications of the hybrid-stress finite element model to plane elasticity problems are examined. Conditions for invariance of the element stiffness are established for two-dimensional problems, the results of which are easily extended to three-dimensional cases. Next, the hybrid-stress functional for a 3-D continuum is manipulated into a more convenient form in which the location of optimal stress/strain sampling points can be identified. To illustrate these concepts, 4- and 8-node plane isoparametric hybrid-stress elements which are invariant and of correct rank are developed and compared with existing hybrid-stress elements. For a 4-node element, lack of invariance is shown to lead to spurious zero energy modes under appropriate element rotation. Alternative 8-node elements are considered, and the best invariant element is shown to be one in which the stress compatibility equations are invoked. Results are also presented which demonstrate the validity of the optimal sampling points, the effects of reduced orders of numerical integration, and the behaviour of the elements for nearly incompressible materials. 相似文献
6.
In this paper, axisymmetric 8-node and 9-node quadrilateral elements for large deformation hyperelastic analysis are devised.
To alleviate the volumetric locking which may be encountered in nearly incompressible materials, a volumetric enhanced assumed
strain (EAS) mode is incorporated in the eight-node and nine-node uniformly reduced-integrated (URI) elements. To control
the compatible spurious zero energy mode in the 9-node element, a stabilization matrix is attained by using a hybrid-strain
formulation and, after some simplification, the matrix can be programmed in the element subroutine without resorting to numerical
integration. Numerical examples show the relative efficacy of the proposed elements and other popular eight-node elements.
In view of the constraint index count, the two elements are analogous to the Q8/3P and Q9/3P elements based on the u–p hybrid/mixed
formulation. However, the former elements are more straight forward than the latter elements in both formulation and programming
implementation. 相似文献
7.
M. Brünig 《Computational Mechanics》1996,18(6):471-484
The present paper is concerned with an efficient framework for a nonlinear finite element procedure for the macroscopic rate-independent
and rate-dependent analysis of micromechanics of metal single crystals undergoing finite elastic-plastic deformations which
is based on the assumption that inelastic deformation is solely due to crystallographic slip. The formulation relies on a
multiplicative decomposition of the material deformation gradient into incompressible elastic and plastic as well as a scalar
valued volumetric part. Furthermore, the crystal deformation is described as arising from two distinct physical mechanisms,
elastic deformation due to distortion of the lattice and crystallographic slip due to shearing along certain preferred lattice
planes in certain preferred lattice directions. Macro- and microscopic stress measures are related to Green’s macroscopic
strains via a hyperelastic constitutive law based on a free energy potential function, whereas plastic potentials expressed
in terms of the generalized Schmid stress lead to a normality rule for the macroscopic plastic strain rate. Estimates of the
microscopic stress and strain histories are obtained via a highly stable and very accurate semi-implicit scalar integration
procedure which employs a plastic predictor followed by an elastic corrector step, and, furthermore, the development of a
consistent elastic-plastic tangent operator as well as its implementation into a nonlinear finite element program will also
be discussed. Finally, the numerical simulation of finite strain elastic-plastic tension tests is presented to demonstrate
the efficiency of the algorithm. 相似文献
8.
A 9-node co-rotational quadrilateral shell element 总被引:2,自引:0,他引:2
A new 9-node co-rotational curved quadrilateral shell element formulation is presented in this paper. Different from other
existing co-rotational element formulations: (1) Additive rotational nodal variables are utilized in the present formulation,
they are two well-chosen components of the mid-surface normal vector at each node, and are additive in an incremental solution
procedure; (2) the internal force vector and the element tangent stiffness matrix are respectively the first derivative and
the second derivative of the element strain energy with respect to the nodal variables, furthermore, all nodal variables are
commutative in calculating the second derivatives, resulting in symmetric element tangent stiffness matrices in the local
and global coordinate systems; (3) the element tangent stiffness matrix is updated using the total values of the nodal variables
in an incremental solution procedure, making it advantageous for solving dynamic problems. Finally, several examples are solved
to verify the reliability and computational efficiency of the proposed element formulation. 相似文献
9.
Ulrich Hueck Peter Wriggers 《International journal for numerical methods in engineering》1995,38(18):3007-3037
A formulation for the plane 4-node quadrilateral finite element is developed based on the principle of virtual displacements for a deformable body. Incompatible modes are added to the standard displacement field. Then expressions for gradient operators are obtained from an expansion of the basis functions into a second-order Taylor series in the physical co-ordinates. The internal degrees of freedom of the incompatible modes are eliminated on the element level. A modified change of variables is used to integrate the element matrices. For a linear elastic material, the element stiffness matrix can be separated into two parts. These are equivalent to a stiffness matrix obtained from underintegration and a stabilization matrix. The formulation includes the cases of plane stress and plane strain as well as the analysis of incompressible materials. Further, the approach is suitable for non-linear analysis. There, an application is given for the calculation of inelastic problems in physically non-linear elasticity. The element is efficient to implement and it is frame invariant. Locking effects and zero-energy modes are avoided as well as singularities of the stiffness matrix due to geometric distortion. A high accuracy is obtained for numerical solutions in displacements and stresses. 相似文献
10.
Henry T. Y. Yang Martin Heinstein J.-M. Shih 《International journal for numerical methods in engineering》1989,28(6):1409-1428
The development and integration of available current methods and the development of new methods for an adaptive finite element analysis of metal forming processes are presented. The analysis includes large-strain, elastic–plastic, and thermal effects. Many numerical methods such as mesh generation, simulation of the contact between the workpiece and tool and die, and optimization of the finite element mesh are integrated and incorporated. In addition, an algorithm is developed which can detect certain severely distorted elements where the area of integration is approaching zero. The advantage of correcting these regions of locally distorted elements is demonstrated. These numerical methods are implemented in a finite element program developed for simulating metal forming processes, with the emphasis on automating the analysis. Examples include an axisymmetric stress simulation of a coldheading process, a plane strain simulation of an extrusion process and a plane strain simulation of orthogonal metal cutting, all with noticeable thermal effects. The orthogonal cutting forces and feed forces calculated are compared with two sets of experimental data, with good agreement. 相似文献
11.
An experimental and numerical study of crack closure 总被引:2,自引:0,他引:2
Fatigue crack propagation and crack closure are studied in Al 2024-T3 under a wide range of ΔK. An elastic-plastic finite element procedure to analyze crack closure for growing cracks is presented. Numerical results are obtained for plane stress and plane strain conditions for different stress ratios. Measurements of opening loads compare well with numerical predictions within the Paris regime. Fractographic observations and compliance measurements indicate that oxide-induced and roughness-induced crack closure substantially increase the opening loads in the near-threshold regime. 相似文献
12.
The combination of a 4-node quadrilateral mixed interpolation of tensorial components element (MITC4) and the cell-based smoothed finite element method (CSFEM) was formulated and implemented in this work for the analysis of free vibration and unidirectional buckling of shell structures. This formulation was applied to numerous numerical examples of non-woven fabrics. As CSFEM schemes do not require coordinate transformation, spurious modes and numerical instabilities are prevented using bilinear quadrilateral element subdivided into two, three and four smoothing cells. An improvement of the original CSFEM formulation was made regarding the calculation of outward unit normal vectors, which allowed to remove the integral operator in the strain smoothing operation. This procedure conducted both to the simplification of the developed formulation and the reduction of computational cost. A wide range of values for the thickness-to-length ratio and edge boundary conditions were analysed. The developed numerical model proved to overcome the shear locking phenomenon with success, revealing both reduced implementation effort and computational cost in comparison to the conventional FEM approach. The cell-based strain smoothing technique used in this work yields accurate results and generally attains higher convergence rate in energy at low computational cost. 相似文献
13.
An elastic-plastic finite element analysis with high order elements is performed to examine closure behaviour of fatigue. cracks in residua1 stress fieids and the numerical results are then compared with experimental results. The finite element analysis, performed under plane stress using 8-node isoparametric elements, can predict fatigue crack closure behaviour through residual stress fields very well. The crack opening and closing behaviour through a compressive residual stress field is found to be complicated and influenced by the applied load magnitude and the location of the crack tip. Three different types of crack opening behaviour, namely, normal, unsymmetric partial and symmetric partial crack opening behaviour are observed through a compressive residual stress field. The partial crack opening stress intensity factor including the partial crack opening effect is recommended for the prediction of fatigue crack growth through a compressive residual stress field. 相似文献
14.
Benedict Verhegghe Graham H. Powell 《International journal for numerical methods in engineering》1986,23(5):863-869
For plane stress/plane strain analysis, the 9-node quadrilateral element performs better than the corresponding 8-node element, especially for non-rectangular shapes. For improved element flexibility and lower computer cost, 2 × 2 quadrature is generally preferable to 3 × 3 quadrature. Unfortunately the 9-node element contains spurious zero-energy modes when under-integrated. A method is proposed to restrain these modes without significant loss of accuracy or added cost. 相似文献
15.
Adnan Ibrahimbegovi Franois Frey Ivica Koar 《International journal for numerical methods in engineering》1995,38(21):3653-3673
Theoretical and computational aspects of vector-like parametrization of three-dimensional finite rotations, which uses only three rotation parameters, are examined in detail in this work. The relationship of the proposed parametrization with the intrinsic representation of finite rotations (via an orthogonal matrix) is clearly identified. Careful considerations of the consistent linearization procedure pertinent to the proposed parametrization of finite rotations are presented for the chosen model problem of Reissner's non-linear beam theory. Pertaining details of numerical implementation are discussed for the simplest choice of the finite element interpolations for a 2-node three-dimensional beam element. A number of numerical simulations in three-dimensional finite rotation analysis are presented in order to illustrate the proposed approach. 相似文献
16.
Expressions for critical timesteps are provided for an explicit finite element method for plane elastodynamic problems in
isotropic, linear elastic solids. Both 4-node and 8-node quadrilateral elements are considered. The method involves solving
for the eigenvalues directly from the eigenvalue problem at the element level. The characteristic polynomial is of order 8
for 4-node elements and 16 for 8-node elements. Due to the complexity of these equations, direct solution of these polynomials
had not been attempted previously. The commonly used critical time-step estimates in the literature were obtained by reducing
the characteristic equation for 4-node elements to a second-order equation involving only the normal strain modes of deformation.
Furthermore, the results appear to be valid only for lumped-mass 4-node elements. In this paper, the characteristic equations
are solved directly for the eigenvalues using <ty>Mathematica<ty> and critical time-step estimates are provided for both lumped
and consistent mass matrix formulations. For lumped-mass method, both full and reduced integration are considered. In each
case, the natural modes of deformation are obtained and it is shown that when Poisson's ratio is below a certain transition value, either shear-mode or hourglass mode of deformation dominates depending on the formulation. And when Poisson's ratio
is above the transition value, in all the cases, the uniform normal strain mode dominates. Consequently, depending on Poisson's
ratio the critical time-step also assumes two different expressions. The approach used in this work also has a definite pedagogical
merit as the same approach is used in obtaining time-step estimates for simpler problems such as rod and beam elements.
Received: 8 January 2002 / Accepted: 12 July 2002
The support of NSF under grant number DMI-9820880 is gratefully acknowledged. 相似文献
17.
《Materials Science & Technology》2013,29(1):70-74
AbstractUnderstanding the thermomechanical phenomena that occur during aluminium extrusion with respect to the variations of temperature, flow stress, strain, and strain rate is of importance for process optimisation. Conventional analytical methods are restricted to the steady state stage of the process and thus cannot provide an insight into the dynamic changes taking place during the initial stage. In the present work, threedimensional simulations using the finite element method were carried out to analyse the development of the deformation zone at the die front and the temperature evolution, before the process attains the steady state. The analysis revealed that a change in friction factor at the billet/container interface from 0.3 to 0.9 enlarges the dead metal zone. However, its size appears unaffected by a change of die orifice shape from round to square at the same reduction ratio. The increase in friction results in an increase of initial extrusion load of about 6%. 相似文献
18.
Shah M. Yunus Sunil Saigal Robert D. Cook 《International journal for numerical methods in engineering》1989,28(4):785-800
A set of three new hybrid elements with rotational degrees-of-freedom (d.o.f.'s) is introduced. The solid, 8-node, hexahedron element is developed for solving three-dimensional elasticity problems. This element has three translational and three rotational d.o.f.'s at each node and is based on a 42-parameter. three-dimensional stress field in the natural convected co-ordinate system. For two-dimensional, plane elasticity problems, an improved triangular hybrid element and a quadrilateral hybrid element are presented. These elements use two translational and one rotational d.o.f. at each node. Three different sets of five-parameter stress fields defined in a natural convected co-ordinate system for the entire element are used for the mixed triangular element. The mixed quadrilateral element is based on a nine-parameter complete linear stress field in natural space. The midside translational d.o.f.'s are expressed in terms of the corner nodal translations and rotations using appropriate transformations. The stiffness matrix is derived based on the Hellinger–Reissner variational principle. The elements pass the patch test and demonstrate an improved performance over the existing elements for prescribed test examples. 相似文献
19.
The dynamic analysis of composite shell structures is carried out by an explicit finite element code employing 4-node one-point quadrature elements. The anisotropic Hoffman yield criterion is adopted to model the laminates. The formulation for stress update using a backward Euler scheme is presented in the plane stress subspace. Several numerical examples are presented. The issue of implementing single-iteration schemes for stress update is also investigated. 相似文献