Kronecker Delta Properties (kronecker + delta_property)

Distribution by Scientific Domains


Selected Abstracts


Integration of geometric design and mechanical analysis using B-spline functions on surface

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 14 2005
Hee Yuel Roh
Abstract B-spline finite element method which integrates geometric design and mechanical analysis of shell structures is presented. To link geometric design and analysis modules completely, the non-periodic cubic B-spline functions are used for the description of geometry and for the displacement interpolation function in the formulation of an isoparametric B-spline finite element. Non-periodic B-spline functions satisfy Kronecker delta properties at the boundaries of domain intervals and allow the handling of the boundary conditions in a conventional finite element formulation. In addition, in this interpolation, interior supports such as nodes can be introduced in a conventional finite element formulation. In the formulation of the mechanical analysis of shells, a general tensor-based shell element with geometrically exact surface representation is employed. In addition, assumed natural strain fields are proposed to alleviate the locking problems. Various numerical examples are provided to assess the performance of the present B-spline finite element. Copyright 2005 John Wiley & Sons, Ltd. [source]


Unequally spaced non-periodic B-spline finite strip method

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 1 2003
Chang-Koon Choi
Abstract The unequally spaced non-periodic B-spline finite strip method (FSM) is presented. The motivation to investigate the irregularly spaced interior nodes in the longitudinal direction of strip is to generalize the concept of non-periodic B-spline FSM and to improve the general accuracy of the stress evaluation in the region of high stress gradients. In the present paper, the unequally spaced non-periodic B3-spline series with multiple knots at the boundary are introduced for the interpolation of displacement and description of geometry in the formulation of isoparametric spline FSM. The use of multiple knots at the boundary makes the shape function satisfy the Kronecker delta properties at the boundary. The unequally spaced B-spline FSM is applied to the stress-reduced shell problem with six degrees of freedom per node. The main purpose of this study is to find a way of ensuring that the geometry of strip is appropriately approximated when the interior nodes of the strip are not regularly spaced along the longitudinal direction. Some numerical results have been compared with those of the previous studies to evaluate the accuracy and efficiency of this method. Copyright 2003 John Wiley & Sons, Ltd. [source]


A reproducing kernel method with nodal interpolation property

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 7 2003
Jiun-Shyan Chen
Abstract A general formulation for developing reproducing kernel (RK) interpolation is presented. This is based on the coupling of a primitive function and an enrichment function. The primitive function introduces discrete Kronecker delta properties, while the enrichment function constitutes reproducing conditions. A necessary condition for obtaining a RK interpolation function is an orthogonality condition between the vector of enrichment functions and the vector of shifted monomial functions at the discrete points. A normalized kernel function with relative small support is employed as the primitive function. This approach does not employ a finite element shape function and therefore the interpolation function can be arbitrarily smooth. To maintain the convergence properties of the original RK approximation, a mixed interpolation is introduced. A rigorous error analysis is provided for the proposed method. Optimal order error estimates are shown for the meshfree interpolation in any Sobolev norms. Optimal order convergence is maintained when the proposed method is employed to solve one-dimensional boundary value problems. Numerical experiments are done demonstrating the theoretical error estimates. The performance of the method is illustrated in several sample problems. Copyright 2003 John Wiley & Sons, Ltd. [source]


Certified solutions for hydraulic structures using the node-based smoothed point interpolation method (NS-PIM)

INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 15 2010
J. Cheng
Abstract A meshfree node-based smoothed point interpolation method (NS-PIM), which has been recently developed for solid mechanics problems, is applied to obtain certified solutions with bounds for hydraulic structure designs. In this approach, shape functions for displacements are constructed using the point interpolation method (PIM), and the shape functions possess the Kronecker delta property and permit the straightforward enforcement of essential boundary conditions. The generalized smoothed Galerkin weak form is then applied to construct discretized system equations using the node-based smoothed strains. As a very novel and important property, the approach can obtain the upper bound solution in energy norm for hydraulic structures. A 2D gravity dam problem and a 3D arch dam problem are solved, respectively, using the NS-PIM and the simulation results of NS-PIM are found to be the upper bounds. Together with standard fully compatible FEM results as a lower bound, we have successfully determined the solution bounds to certify the accuracy of numerical solutions. This confirms that the NS-PIM is very useful for producing certified solutions for the analysis of huge hydraulic structures. Copyright 2009 John Wiley & Sons, Ltd. [source]


Moving kriging interpolation and element-free Galerkin method

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 1 2003
Lei Gu
Abstract A new formulation of the element-free Galerkin (EFG) method is presented in this paper. EFG has been extensively popularized in the literature in recent years due to its flexibility and high convergence rate in solving boundary value problems. However, accurate imposition of essential boundary conditions in the EFG method often presents difficulties because the Kronecker delta property, which is satisfied by finite element shape functions, does not necessarily hold for the EFG shape function. The proposed new formulation of EFG eliminates this shortcoming through the moving kriging (MK) interpolation. Two major properties of the MK interpolation: the Kronecker delta property (,I(sJ)=,IJ) and the consistency property (,In,I(x)=1 and ,In,I(x)xIi=xi) are proved. Some preliminary numerical results are given. Copyright 2002 John Wiley & Sons, Ltd. [source]