共查询到20条相似文献，搜索用时 15 毫秒
1.
I. Pitacco 《International journal for numerical methods in engineering》2007,72(2):156-179
A new approach to derive finite elements for the thin plate model is presented. The proposed method approximates compatible Kirchhoff formulations by means of orthogonal polynomials expansion of the curvature field depending only on the element boundary traces. With respect to the compatible formulation the proposed method produces elements that beneficially underestimate the deformation energy. A simple triangular element is developed and investigated from both the theoretical and the numerical point of view and numerically compared with other two well‐known elements. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献
2.
B. Boroomand M. Ghaffarian O. C. Zienkiewicz 《International journal for numerical methods in engineering》2004,61(10):1644-1673
In this paper a study is performed on application of two recovery methods, i.e. superconvergent patch recovery (SPR) and the recovery by equilibrium of patches (REP), to plate problems. The two recovery methods have been recognized to give similar results in adaptive solutions of two dimensional stress problems. While the former applies a least square fit over a set of values at the so called superconvergent points, the latter does not need any knowledge of such points and thus has a wider application especially in non‐linear problems. The formulation of REP is extended to Reissner–Mindlin plate problems. The convergence rates of the recovered fields of the gradients obtained from application of the two methods are compared using series of regular triangular and rectangular meshes for thick and thin plate solution cases. Assumed strain formulation based elements, i.e. the elements formulated by mixed interpolation of tensorial components, as well as conventional from of elements based on selective integration schemes are employed for the study. In order to investigate the possibility of any improvement in the results by adding equilibrium constraints to SPR, as some authors suggest for simple two‐dimensional problems, some weighted forms of such conditions are designed and added to the formulation. Comprehensive study has been given first by varying the weight terms to obtain the best enhanced results and then using the optimal values to investigate the effects of the constraints on the rate of convergence. It is observed that despite of the cost of this approach, due to the coupling of the gradient terms, no significant improvement is achieved. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献
3.
M. L. Bittencourt M. G. Vazquez T. G. Vazquez 《International journal for numerical methods in engineering》2007,71(5):529-563
This paper presents an uniform and unified approach to construct h- and p-shape functions for quadrilaterals, triangles, hexahedral and tetrahedral based on the tensorial product of one-dimensional Lagrange and Jacobi polynomials. The approach uses indices to denote the one-dimensional polynomials in each tensorization direction. The appropriate manipulation of the indices allows to obtain hierarchical or non-hierarchical and inter-element C0 continuous or non-continuous bases. For the one-dimensional elements, quadrilaterals, triangles and hexahedral, the optimal weights of the Jacobi polynomials are determined, the sparsity profiles of the local mass and stiffness matrices plotted and the condition numbers calculated. A brief discussion of the use of sum factorization and computational implementation is considered. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
4.
Tinh Quoc Bui Tan Nhat Nguyen Hung Nguyen‐Dang 《International journal for numerical methods in engineering》2009,77(10):1371-1395
This paper mainly proposes an alternative way for numerical implementation of thin plates bending based on a new improvement of meshless method, which is combined between the standard element‐free Galerkin method and one different shape functions building technique. The moving Kriging (MK) interpolation is applied instead of the traditional moving least‐square approximation in order to overcome Kronecker's delta property where the standard method does not satisfy. Obviously, the deflection of the thin plates is approximated via the MK interpolation. To illustrate this approach, numerical analysis is examined in both regular and irregular systems. Three examples with different geometric shapes of thin plates undergoing a simply supported boundary are performed. In addition, two important parameters of the present method are also analyzed. A good agreement can be found among the proposed, analytical and finite element methods. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
5.
J.P. Moitinho de Almeida E.A.W. Maunder Carlos Tiago 《International journal for numerical methods in engineering》2019,120(1):56-85
We revisit compatible finite element formulations for Kirchhoff plates and propose a new general degree hybridized approach that strictly imposes C1 continuity. These new elements are triangular and based on nodal polynomial approximation functions that only use displacement and rotation degrees of freedom for assembly, and thereby “nearly” impose C1 continuity. This condition is then strictly enforced by adding appropriately chosen hybrid constraints and the corresponding Lagrange multipliers. Unlike all other existing approaches, this formulation allows for the definition of elements of arbitrary degree considering a single polynomial basis for each element, without using degrees of freedom associated with second-order derivatives. The convergence is compared with that of alternative approaches in terms of numbers of elements and degrees of freedom. 相似文献
6.
This article presents the formulation of a finite element method for nonlinear Kirchhoff rods, based on a G1$$ {G}^1 $$ interpolation of the rod's geometry in terms of Hermite shape functions. The critical use of the same interpolation scheme for both the geometry and the kinematics of the rod is shown to lead to the correct invariant properties of the final numerical formulation, thus leading to the correct resolution of the fundamental equilibrium relations along it (balance of forces and moments). The so-called “self-straining” is completely avoided. Several numerical examples are presented illustrating the adequacy of the proposed formulation for the analysis of thin rods undergoing large finite deformations. 相似文献
7.
该文采用满足Kirchhoff假设的薄板理论,推导了各向异性材料系列解析试函数,并利用该系列解析试函数构造了一个四边形应力杂交板单元。首先,该文从薄板理论的基本方程出发,推导了各向异性材料薄板中面挠度w应满足的特征微分方程。然后,从该方程出发求得w的系列特征通解,由w特征通解可进一步求得广义位移、广义应变和广义应力的解析试函数。同时,根据广义应力利用平衡条件构造了相应的横向剪力解析试函数。最后,根据已有的广义应力和横向剪力解析试函数构造了一个四边形应力杂交板单元ATF-PH4。数值算例表明:上述方法构造出的单元模型有很好的精度、收敛性,且对网格畸变不敏感,同时能较好地解决板单元的厚薄通用性问题。 相似文献
8.
M. L. Bittencourt 《International journal for numerical methods in engineering》2005,63(11):1530-1558
This paper presents nodal and modal shape functions for triangle and tetrahedron finite elements. The functions are constructed based on the fully tensorial expansions of one‐dimensional polynomials expressed in barycentric co‐ordinates. The nodal functions obtained from the application of the tensorial procedure are the standard h‐Lagrange shape functions presented in the literature. The modal shape functions use Jacobi polynomials and have a natural global C0 inter‐element continuity. An efficient Gauss–Jacobi numerical integration procedure is also presented to decrease the number of points for the consistent integration of the element matrices. An example illustrates the approximation properties of the modal functions. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
9.
Attilio Frangi Marc Bonnet 《International journal for numerical methods in engineering》1998,41(2):337-369
A variational Boundary Element formulation is proposed for the solution of the elastic Kirchhoff plate bending problem. The stationarity conditions of an augmented potential energy functional are first discussed. After addressing the topic of the choice of the test functions, a regularization process based on integrations by parts is developed, which allows to express the formulation in terms of double integrals, the inner being at most weakly singular and the outer regular. Standard integration procedures may then be applied for their numerical evaluation in the presence of both straight and curved boundaries. The normal slope and the vertical displacement must be C0 and C1 continuous, respectively. Numerical examples show, through comparisons with analytical solutions, that a high accuracy is achieved. © 1998 John Wiley & Sons, Ltd. 相似文献
10.
H. Hashemolhosseini N. Sadati M. Farzin 《International journal for numerical methods in engineering》2002,53(8):1781-1800
A new class of Cn continuous interpolations is presented. These interpolations consist of two or more Lagrangian interpolations blended by pseudo Hermitian interpolation. Using this class of interpolations a new Cn family of displacement type elements is developed. The properties of this new family of elements such as their precision and their superconvergent points are discussed. Some solutions to the corner elements problem and implication of different boundary conditions are proposed. Using this new kind of element, several examples of deflection of elastic beams and plates are treated, the results of which are encouraging. Copyright © 2001 John Wiley & Sons, Ltd. 相似文献
11.
Peter Hansbo David Heintz Mats G. Larson 《International journal for numerical methods in engineering》2010,81(5):584-603
We present a discontinuous finite element method for the Kirchhoff plate model with membrane stresses. The method is based on P2‐approximations on simplices for the out‐of‐plane deformations, using C0‐continuous approximations. We derive a posteriori error estimates for linear functionals of the error and give some numerical examples. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
12.
K. Y. Sze W. C. Yuan Y. X. Zhou 《International journal for numerical methods in engineering》2020,121(16):3660-3679
Computational analyses of gradient-elasticity often require the trial solution to be C1 yet constructing simple C1 finite elements is not trivial. This article develops two 48-dof 4-node tetrahedral elements for 3D gradient-elasticity analyses by generalizing the discrete Kirchhoff method and a relaxed hybrid-stress method. Displacement and displacement-gradient are the only nodal dofs. Both methods start with the derivation of a C0 quadratic-complete displacement interpolation from which the strain is derived. In the first element, displacement-gradient at the mid-edge points are approximated and then interpolated together with those at the nodes whilst the strain-gradient is derived from the displacement-gradient interpolation. In the second element, the assumed constant double-stress modes are employed to enforce the continuity of the normal derivative of the displacement. The whole formulation can be viewed as if the strain-gradient matrix derived from the displacement interpolation matrix is refined by a constant matrix. Both elements are validated by the individual element patch test and other numerical benchmark tests. To the best knowledge of the authors, the proposed elements are probably the first nonmixed/penalty 3D elements which employ only displacement and displacement-gradient as the nodal dofs for gradient-elasticity analyses. 相似文献
13.
刘孝书 《海军工程学院学报》2006,18(6):18-20
运用Nevanlinna的亚纯函数理论方法，研究了亚纯函数微分多项式的值的分布理论，获得了若f（z）是超越亚纯函数,φ是关于f的微分多项式，满足条件N（r,f）＋N（r,1/f）=S（r,f）,关于φ零点的几个结果，改进并推广了YangCC和仪洪勋等人的有关结果． 相似文献
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15.
The Kirchhoff approximation is used to show that the time domain impulse response of an isolated flat crack can be given a simple geometrical interpretation in terms of the derivative of a projected length function. For an elliptical crack, this derivative can be obtained explicitly to yield the two edge-diffracted waves which originate from the flashpoints of the crack. An explicit coordinate invariant expression is obtained from this elliptical crack solution which relates the time difference, t, between the arrival of these edge-diffracted waves and the crack size and orientation. Previously, we have proposed that this expression, together with t measurements in different scattering directions, could be used in a regression analysis as the basis for performing a constrained inversion of crack scattering data (i.e., where we attempt to obtain the best equivalent flat elliptical crack that fits the scattering measurements). Here we will demonstrate some results of applying the proposed algorithm using noisy synthetic data. The sensitivity of the results to both, number of measurements and transducer orientation, will be discussed. 相似文献
16.
In this paper, a deep collocation method (DCM) for thin plate bending problems is proposed. This method takes advantage of computational graphs and backpropagation algorithms involved in deep learning. Besides, the proposed DCM is based on a feedforward deep neural network (DNN) and differs from most previous applications of deep learning for mechanical problems. First, batches of randomly distributed collocation points are initially generated inside the domain and along the boundaries. A loss function is built with the aim that the governing partial differential equations (PDEs) of Kirchhoff plate bending problems, and the boundary/initial conditions are minimised at those collocation points. A combination of optimizers is adopted in the backpropagation process to minimize the loss function so as to obtain the optimal hyperparameters. In Kirchhoff plate bending problems, the C1 continuity requirement poses significant difficulties in traditional mesh-based methods. This can be solved by the proposed DCM, which uses a deep neural network to approximate the continuous transversal deflection, and is proved to be suitable to the bending analysis of Kirchhoff plate of various geometries. 相似文献
17.
A design methodology based on the adjoint approach for flow problems governed by the incompressible Euler equations is presented. The main feature of the algorithm is that it avoids solving the adjoint equations, which saves an important amount of CPU time. Furthermore, the methodology is general in the sense it does not depend on the geometry representation. All the grid points on the surface to be optimized can be chosen as design parameters. In addition, the methodology can be applied to any type of mesh. The partial derivatives of the flow equations with respect to the design parameters are computed by finite differences. In this way, this computation is independent of the numerical scheme employed to obtain the flow solution. Once the design parameters have been updated, the new solid surface is obtained with a pseudo‐shell approach in such a way that local singularities, which can degrade or inhibit the convergence to the optimal solution, are avoided. Some 2D and 3D numerical examples are shown to demonstrate the proposed methodology. Copyright © 2001 John Wiley & Sons, Ltd. 相似文献
18.
Computational analysis of gradient elasticity often requires the trial solution to be C1, yet constructing simple C1 finite elements is not trivial. In this paper, three four-node 24-DOF quadrilateral elements for gradient elasticity analysis are devised by generalizing some of the advanced element formulations for thin-plate analysis. These include the discrete Kirchhoff method, a relaxed hybrid-stress method, and the hybrid-stress method with equilibrating internal force modes. The first two methods start with the derivation of a C0 displacement, which is quadratic complete in the Cartesian coordinates. In the first method, at the midside points are derived and interpolated together with those at the nodes. Strain is derived from the displacement interpolation yet the second-order displacement derivatives are derived from the displacement-gradient interpolation. In the second method, only the assumed constant double-stress modes are employed to enforce the continuity of the normal derivative of the displacement. In the third method, the equilibrating internal force modes require the C1 displacement to be defined only along the element boundary and the domain interpolation can be avoided. Patch test involving linear stress and constant double stress as well as other tests are presented to validate the proposed elements. 相似文献
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20.
A new discrete Kirchhoff quadrilateral element based on the refined third-order theory is developed for the analysis of composite plates. The element has seven degrees of freedom per node, namely, the three displacements, two rotations and two transverse shear strain components at the mid-surface. The inplane displacements and the shear strains are interpolated using bilinear interpolation functions and the mid-surface rotations are interpolated using bi-quadratic functions based on the discrete Kirchhoff technique. The element stiffness matrix and the consistent load vector are developed using the principle of virtual work. The finite element formulation is validated by comparing the results for simply-supported plate with the analytical Navier solution. Comparison of the present results with those using other available elements based on the TOT establishes the superiority of the present element in respect of simplicity, accuracy and computational efficiency. The element is free from shear locking 相似文献