Turgut Tokdemir

UNSTRUCTURED GRID GENERATION AND A SIMPLE TRIANGULATION ALGORITHM FOR ARBITRARY 2-D GEOMETRIES USING OBJECT ORIENTED PROGRAMMING

This paper describes the logic of a dynamic algorithm for a general 2D Delaunay triangulation of arbitrarily prescribed interior and boundary nodes. The complexity of the geometry is completely arbitrary. The scheme is free of specific restrictions on the input of the geometrical data. The scheme generates triangles whose associated circumcircles contain no nodal points except their vertices. There is no predefined limit for the number of points and the boundaries. The direction of generation of the triangles cannot be determined a priori as opposed to the moving front techniques. An automatic node placement scheme reflecting the initial boundary point spacings is used. The successive refinement scheme results in such a point distribution that the triangulation algorithm need not perform any geometric intersection check for overlapped triangles and penetrated boundaries. Further computational saving is provided by using a special binary tree (ADT) in which the points are ordered such that contiguous points in the list are neighbours in physical space. The method consists of a set of simple rules to understand. The dynamic nature of the Object Oriented Programming (OOP) of the algorithms provides efficient memory management on the insertion, deletion and searching processes. The computational effort bears a linear relation-ship between the CPU time and the total number of nodes. Some of the existing methods in the literature regarding triangular mesh generation are discussed in context.

Simultaneous, finite, gyroscopic and radial oscillations of hyperelastic cylindrical tubes

Abstract Simultaneous, finite, gyroscopic and radial oscillations of long, circular cylindrical tubes are investigated. The material of the tube is assumed to be homogeneous, isotropic, hyperelastic and incompressible. The theory of finite elasticity is used in the formulation of the problem. The motion is started by a sudden release of the tube which is subjected to an initial finite gyroscopic twist. The condition of material incompressibility is used to reduce the governing equations into a set of two non-linear, integro-differential equations where the radial motion is characterized by that of a single degree of freedom system. These equations, together with the appropriate initial and boundary conditions, are solved numerically by a finite element scheme.

Modeling of Asymmetric Shear Wall-Frame Building Structures

Abstract Based on the conventional wide column analogy, two different three-dimensional shear wall models for open and closed sections are proposed. These approximate models are verified in comparison to not only the results available in the literature but also the ones obtained by using models containing shell elements. With the help of these new models five different groups of shear wall-frame structures with different floor plans and different heights are analyzed. The first three natural vibration periods are determined and time history analyses are performed. The results of these computations are observed to be in good agreement with those obtained by detailed models containing shell elements.

Stability and vibrations of layered, compressible hyperelastic, rectangular columns

The stability and the small vibrations of rectangular, layered columns undergoing finite axial deformations are investigated, by using the theory of finite elasticity. The layers of the column are assumed to be made of compressible, hyperelastic materials. Some numerical results of the closed form solutions are provided to study the effect of material and geometric properties.

On the Modeling of Nonplanar Shear Walls in Shear Wall - Frame Building Structures

The objective of this study is to model the non-planar shear walls of asymmetric shear wall-frame building structures in elastic range. The modeling work is based on open and closed sections shear wall assemblies for which two different three-dimensional models are developed and verified in comparison to common shear wall modeling techniques.

TRANSIENT RESPONSE OF POINT-EXCITED SUBMERGED ELLIPSOIDAL SHELLS USING IMPROVED TRANSMITTING BOUNDARIES

Transient response of ellipsoidal shells submerged in an acoustic medium subjected to a concentrated Heaviside load at the apex is studied numerically using improved transmitting boundaries. By employing the rigorous Residual Variable Method, the second derivative in the wave equation with respect to the spatial variable extending to infinity is eliminated. The resulting modified equation is an exact boundary condition nonlocal in space requiring modal analysis. The ellipsoidal shell is considered to be enclosed by an artificial spherical truncation surface in the fluid domain on which the improved transmitting boundary condition is used. The effect of the ratio between the two radii of the submerged ellipsoidal shells on the apex deflection and on the hydrodynamic pressure at the apex is investigated. Numerical results obtained by incorporating improved transmitting boundary conditions into the finite element program are presented in graphical forms and discussed.

A simple unstructured tetrahedral mesh generation algorithm for complex geometries

This paper describes the logic of a dynamic algorithm for a general 3D tetrahedrization of an arbitrarily prescribed geometry. The algorithm requires the minimal surface information. The solid modelling of the 3D objects needs not to be given in full explicit connectivity definitions of the surface triangles. The generated tetrahedrons have empty circumspheres which are the indication of the Delaunay property. A new automatic node replacement scheme reflecting the initial surface nodal spacings is developed. The successive refinement scheme results in such a point distribution that the algorithm does not require any surface conforming checks to avoid penetrated surface boundaries and overlapped tetrahedrons. The surface triangles become a direct consequence of interior tetrahedrization. The rules of the generation algorithm are simple to understand and to program. Some of the existing methods in the literature and the effectiveness of the geometric searching strategies are discussed in the context.

Extension of the residual variable method to propagation problems and its application to the diffusion equation in spherical coordinates

SummaryWe consider a partial differential equation in spherical (cylindrical) coordinates describing a dynamic process in an infinite medium with an inner spherical (cylindrical) boundary. If an analytical solution is not possible to obtain, then one resorts to numerical techniques. In this case it becomes necessary to discretize the infinite domain even if the solution is required on the inner spherical (cylindrical) surface or at a limited number of points in the domain only. The Residual Variable Method (RVM) circumvents the difficulty of discretizing the infinite domain. The governing equation is integrated once in radial direction. The number of the spatial dimensions is, thus, reduced by one. It is now possible to determine the solution on the inner boundary without having to deal with the infinite domain. The RVM is amenable to “marching” solutions in a finite-difference implementation and it is suitable for the analysis of propagation into the infinite medium from the inner surface. There is no need to discretize the infinite domain in its entirety at all. The propagation analysis can be terminated at any point in the radial direction without having to consider the rest.

Extension of the residual variable method to propagation problems and its application to the wave equation in cylindrical coordinates

Abstract Consider a partial differential equation with cylindrical coordinates describing a dynamic process in an infinite medium with an inner cylindrical boundary. If an analytical solution to the problem is not possible, then one resorts to numerical techniques. In this case it becomes necessary to discretize the infinite domain even if the solution is required on the inner cylindrical surface or at a limited number of points in the domain only. The residual variable method (RVM) circumvents the difficulty associated with the discretization of the infinite domain. In essence, the governing equation is integrated once in a radial direction. The number of the spatial dimensions of the problem is reduced by one. It is now possible to determine the solution on the inner boundary without having to deal with the infinite domain. It is shown in this paper that the RVM is amenable to ‘marching’ solutions in a finite-difference implementation and that it is suitable for the analysis of propagation into the infinite medium from the inner surface. There is no need to discretize the infinite domain in its entirety at all. The propagation analysis can be terminated at any point in the radial direction without having to consider the rest.