Worsak Kanok-Nukulchai

A finite element method for a class of contact-impact problems

Abstract We present a finite element method for a class of contact-impact problems. Theoretical background and numerical implementation features are discussed. In particular, we consider the basic ideas of contact-impact, the assumptions which define the class of problems we deal with, spatial and temporal discretizations of the bodies involved, special problems concerning the contact of bodies of different dimensions, discrete impact and release conditions, and solution of the nonlinear algebraic problem. Several sample problems are presented which demonstrate the accuracy and versatility of the algorithm.

FURTHER INVESTIGATION OF ELEMENT-FREE GALERKIN METHOD USING MOVING KRIGING INTERPOLATION

Following its first introduction, this study further scrutinizes the new type of shape functions for Element-free Galerkin Method (EFGM) based on the Moving Kriging (MK) interpolation. Kriging is a geostatistical method of spatial interpolation. Its basic premise is that every unknown point can be interpolated from known scattered points in its specified neighborhood. This property is ideal for EFGM. Previously, a shortcoming of EFGM based on Moving Least Square (MLS) approximation is associated with its limitation to satisfy essential boundary conditions exactly. With MK interpolation functions, EFGM solution can satisfy essential boundary conditions automatically. Numerical tests on one and two-dimensional elasticity problems have confirmed the effectiveness of MK in addressing this specific shortcoming of EFGM. Furthermore, the study also finds the accuracy of EFGM to be greatly enhanced with the use of MK shape functions.

A large deformation formulation for shell analysis by the finite element method

Abstract A total Lagrangian formulation for large deformation analysis of shells by the finite element method is presented. The development of the model is based upon the three dimensional field equations. To permit solution of shell problems without numerical difficulties, a special discretization in the thickness direction is employed. The displacement field of the shell element is represented by the displacement on the shell midsurface together with the relative displacement on the shell top surface, without resorting to the more complicating finite rotation parameters. Consistent linearization of the discretized balance equations is used to establish a Newton-Raphson solution scheme. The versatility and accuracy of the present shell element are demonstrated by solving several numerical examples.

A nine-node assumed strain finite element for large-deformation analysis of laminated shells

An application of the element-based Lagrangian formulation is described for large-deformation analysis of both single-layered and laminated shells. Natural co-ordinate-based stresses, strains and constitutive equations are used throughout the formulation of the present shell element which offers significant implementation advantages compared with the traditional Lagrangian formulation. In order to avoid locking phenomena, an assumed strain method has been employed with judicious selection of the sampling points. Three strictly successive finite rotations are used to represent the current orientation of the shell normal. The equivalent natural constitutive equation is derived using an explicit transformation scheme to consider the multi-layer effect of laminated structures. The arc-length control method is used to trace complex load-displacement paths. Several numerical analyses are presented and discussed in order to investigate the capabilities of the present shell element.

A MESHLESS ANALYSIS OF SHELLS BASED ON MOVING KRIGING INTERPOLATION

An Element Free Galerkin Method (EFGM) for the analysis of degenerated shell structures is presented. The method is based on the Moving Kriging (MK) Interpolation function. The properties of the interpolation function possess the Kronecker delta property. With the MK Interpolation function no additional treatment required at the boundary conditions compared with that of using Moving Least Square (MLS) approximation. This deficiency of MLS at boundary condition has been definitely eradicated. The membrane and shear locking in the numerical analysis for degenerated shell problems has been alleviated by using higher order and removed by using quartic order of polynomials. Numerical benchmark examples for shell structures are presented to validate the proposed approach.

AN ENHANCEMENT OF FINITE ELEMENT METHOD WITH MOVING KRIGING SHAPE FUNCTIONS

This paper presents an enhancement of the finite element method (FEM) by adopting the moving Kriging (MK) interpolation as a substitute for the traditional hat functions. The MK shape functions can be referred as element-free because their construction is not tied to the element geometry. Kriging interpolation is a geostatistical technique for spatial interpolation. The basic idea of Kriging is that any unknown point can be interpolated from known scatter points in a specific domain. Using the moving Kriging interpolation, shape functions can be generated over any finite set of nodes. This leads to an idea to extend the influence of a node beyond the layer of surrounding elements to enhance the global smoothness of the field variable and its derivatives. The present paper thus proposes a concept of layered domain of influence. Hence, characteristic arrays of an element, such as the element stiffness, have contributions from all visible nodes that include a set of satellite nodes unattached to the element. The validation of the method was confirmed through numerical tests of one and two-dimensional problems. The results show remarkable accuracy and global smoothness. Existing general-purposed FE programs can be easily modified to accommodate this new element concept; thus, the method has a higher chance to be accepted in practice.

MATHEMATICAL MODELLING OF CABLE-STAYED BRIDGES

Modern cable-stayed bridge construction involves the assembly of an almost unlimited variety of deck, pylon and cable elements together, in a multitude of different ways. For their static and dynamic analyses, the application of accurate and efficient mathematical models are essential. This paper presents various methods for modelling components of cable-stayed bridges, i.e., the cables, deck, pylon and joints, as well as the assembly of these components into a complete bridge model for general computer analysis. The use of appropriate finite elements for detailed analysis of deck units is also presented.

Nonlinear modelling of cable-stayed bridges

This paper presents an application of a powerful thin-walled element and a special cable element for three-dimensional modelling of steel cable-stayed bridges. Both linear and nonlinear effects are considered, as geometric nonlinearity may arise from the finite displacement of the bridge deck as well as the cables. As cable-stayed bridge decks are normally built-up thin-walled cross-sections, the effects of flexural-torsion coupling as well as warping restraint are included. Finally, several examples of cable-stayed bridges serve to demonstrate the effectiveness of this most comprehensive model.

ON THE CONVERGENCE OF THE KRIGING-BASED FINITE ELEMENT METHOD

An enhancement of the FEM using Kriging interpolation (K-FEM) was recently proposed. This method offers advantages over the conventional FEM and mesh-free methods. With Kriging interpolation, the approximated field over an element is influenced not only by its own element nodes but also by a set of satellite nodes outside the element. This results in incompatibility along interelement boundaries. Consequently, the convergence of the solutions is questionable. In this paper, the convergence is investigated through several numerical tests. It is found that the solutions of the K-FEM with an appropriate range of parameters converge to the corresponding exact solutions.

Element-based lagrangian formulation for large-deformation analysis

Abstract This paper introduces a new variation of the Lagrangian formulation for large-deformation analysis of continua and structures. For each individual element in the deformed mesh, the standard parental element will be used as its reference configuration. With a new definition of “natural-coordinate-based” stress, strain and constitutive tensors associated with the simple domain of the parental element, the expressions for element characteristics appear in a simpler form than that of the conventional Lagrangian approach. This alternative form of formulation will be referred to as the Element-Based Lagrangian Formulation (ELF). It not only serves as an elegant alternative to the traditional approach, but also offers certain implementational advantages.