Tension Structures

Analysis of 3D hyperelastic membrane structures

This text presents a definition of the deformation gradient tensor for the triangular element. Download the complete text as MS-Word and PDF documents, computer source code written in Ada95 and executable code for Windows. The following three examples are compared with the ANSYS software package: plane strain with compressible neo-hookean material, plane stress with incompressible neo-hookean material and plane stress with compressible neo-hookean material (work in progress).


LIGHTS computer code

LIGHTS is a public domain 3D finite element program for the design and analysis of light structures. The program element library includes cable elements, membrane element, frame element and spring element. The computer code generates a script file for AutoCAD. A simple user's manual has been included in the documentation. It is currently under development and not yet fully tested. It is the responsibility of the user to confirm the accuracy and usefulness of the results. It was last updated on Sep/07/2006. Download the source code written in Ada95, examples and executable code for Windows. The theory for this computer code is explained in the following three articles:


Minimizing total potential energy to find equilibrium

The stable equilibrium configurations of a structure are associated with the local minimum points of its total potential energy. There is a fundamental difference between solving the equilibrium equation and minimizing the total potential energy. The advantages of the energy approach are: It is not necessary to derive the stiffness matrix expressions. It is not necessary to solve any system of equations. It does not matter if the structure is a mechanism, which is frequently the case of tension structures. Download the complete text as MS-Word and PDF documents (work in progress).


A simple procedure for analysis of cable network structures

This text presents a mathematical modeling of a cable finite element. It includes a total Lagrangian description using the Engineering strain definition and assumes an elastic material (linear or nonlinear). A procedure to analyze a cable network in the presence of conservative forces and small deformations is summarized. Mathematical programming techniques make the use of stiffness matrix pointless. Download the complete text as MS-Word and PDF documents, computer source code written in Ada95 and executable code for Windows. The computer code generates a script file for AutoCAD. A version of this work was published in the Proceedings of the Fifth International Conference on Space Structures, Thomas Telford, 2002.


A simple procedure for shape finding and analysis of fabric structures

This text presents a mathematical modeling of a membrane finite element. It includes a total Lagrangian description using the Green strain definition and assumes a linear elastic material. A procedure to define the shape of a fabric structure and to analyze it in the presence of conservative forces and small deformations is summarized. The shapes are generated by loading a membrane with concentrated forces, distributed force and also by prescribing displacements. Mathematical programming techniques make the use of stiffness matrix pointless. Download the complete text as MS-Word and PDF documents, computer source code written in Ada95 and executable code for Windows. The computer code generates a script file for AutoCAD. A version of this work was published in the Proceedings of the Fifth International Conference on Space Structures, Thomas Telford, 2002.

Analysis of 3D isotropic membrane structures

This text presents a mathematical modeling of an isotropic membrane finite element. It includes a total Lagrangian description with a linear elastic material, using either the Green or Engineering strain definition. Mathematical programming techniques make the use of stiffness matrix pointless. Download the complete text as MS-Word and PDF documents, computer source codes written in Ada95 and executable codes for Windows. The computer codes generate a script file for AutoCAD.

Analysis of 3D orthotropic membrane structures

This text presents a mathematical modeling of an orthotropic membrane finite element. It includes a total Lagrangian description with a linear elastic material, using either the Green or Engineering strain definition. Mathematical programming techniques make the use of stiffness matrix pointless. Download the complete text as MS-Word and PDF documents, computer source codes written in Ada95 and executable codes for Windows. The computer codes generate a script file for AutoCAD. This is a work in progress and it was last updated on Jan/22/2007.

Finite element analysis for minimal shape

This text presents a mathematical model for minimizing path length, surface area and volume using a line element, a triangle element and a tetrahedron element respectively. The triangle element together with the line element can be used to minimize a surface area with free boundaries through the unifying concept of minimizing shape volume. A quasi-Newton method is used, which avoids the evaluation of the Hessian matrix. Download the complete text as MS-Word and PDF documents, computer source codes written in Ada95 and executable codes for Windows. The computer codes generate a script file for AutoCAD.