A platform for research: civil engineering, architecture and urbanism
A platform for research: civil engineering, architecture and urbanism
Body-oriented coordinates applied to the finite-element method
Abstract The objective of this research is to increase the accuracy of the finite-element method using coordinates intrinsic to the shape of the body being analyzed. We refer to these coordinates as body coordinates. Existing finite elements use Cartesian coordinates and are more accurate for solving rectangular shaped problems than for solving nonrectangular-shaped problems. To check the feasibility of this research, we developed finite-element codes that used both cylindrical and Cartesian coordinates to solve problems in which the bodies were cylindrical-spaped. We obtained the most accurate solutions using the code that used cylindrical coordinates. Body coordinates become Cartesian coordinates for rectangular-spaped bodies and cylindrical coordinates for circular-shaped bodies. The body coordinate's finite-element formulation uses coordinate transformations from the body to the Cartesian coordinates. These transformations are developed using blending functions and boundary functions. Gradients of the Cartesian coordinates, with respect to body coordinates, are needed for stiffness calculations. Thus, the criterion for the blending function derivation is ‘the nearest boundaries dominate’, both for coordinate transformations and for gradient of coordinate transformations. For our studies, we developed two codes, one that uses body coordinates and one that uses Cartesian coordinates. These codes have been used to solve six example problems.
Body-oriented coordinates applied to the finite-element method
Abstract The objective of this research is to increase the accuracy of the finite-element method using coordinates intrinsic to the shape of the body being analyzed. We refer to these coordinates as body coordinates. Existing finite elements use Cartesian coordinates and are more accurate for solving rectangular shaped problems than for solving nonrectangular-shaped problems. To check the feasibility of this research, we developed finite-element codes that used both cylindrical and Cartesian coordinates to solve problems in which the bodies were cylindrical-spaped. We obtained the most accurate solutions using the code that used cylindrical coordinates. Body coordinates become Cartesian coordinates for rectangular-spaped bodies and cylindrical coordinates for circular-shaped bodies. The body coordinate's finite-element formulation uses coordinate transformations from the body to the Cartesian coordinates. These transformations are developed using blending functions and boundary functions. Gradients of the Cartesian coordinates, with respect to body coordinates, are needed for stiffness calculations. Thus, the criterion for the blending function derivation is ‘the nearest boundaries dominate’, both for coordinate transformations and for gradient of coordinate transformations. For our studies, we developed two codes, one that uses body coordinates and one that uses Cartesian coordinates. These codes have been used to solve six example problems.
Body-oriented coordinates applied to the finite-element method
Cook, W.A. (author)
Engineering Analysis ; 5 ; 2-11
1988-01-01
10 pages
Article (Journal)
Electronic Resource
English
Finite Element Solution of Non-Linear Splines Using Intrinsic Coordinates
| British Library Conference Proceedings | 1993
A finite element in elliptic coordinates with application to membrane vibration
| Online Contents | 2005
Object-Oriented Finite Element Analysis
| British Library Conference Proceedings | 1996
Object Oriented Finite Element Analysis (II) the Finite Element Procedure
| British Library Conference Proceedings | 1995