# Structural Computations by Using SVD

• Buntara Sthenly Gan
Chapter

## Abstract

In this chapter, we will learn about the procedure, algorithm, and technique in the numerical analysis to obtain solutions of the structural computations by using the singular value decomposition (SVD) method to analyze the equilibrium matrix of the structure which is based on the force density method (FDM). The algorithm to solve the structural system depends on the classification of the structures based on the degree of static and kinematic properties. By using SVD which make use of FDM, a structural system which has the singularity such as rigid body motion can also be analyzed. Thus, the SVD is suitable for use to analyze the system of tensegrity structures in general. Examples of the structural system classes accompanied by the MATLAB codes are presented.

## Keywords

Structural system Singular value decomposition Structural analysis Equilibrium matrix Force density method

## References

1. Pellegrino S (1990) Analysis of prestressed mechanisms. Int J Solids Struct 26(12):1329–1350
2. Pellegrino S (1993) Structural computations with the singular value decomposition of the equilibrium matrix. Int J Solids Struct 30(21):3025–3035
3. Pellegrino S, Calladine CR (1986) Matrix analysis of statically and kinematically indeterminate frameworks. Int J Solids Struct 22(4):409–428
4. Pellegrino S, Van Heerden TF (1990) Solution of equilibrium equations in the force method: a compact band method for underdetermined linear systems. Comput Struct 37:743–751
5. Schek HJ (1974) The force density method for form finding and computation of general networks. Comput Methods Appl Mech Eng 3:115–134

1. Gradshteyn IS, Ryzhik IM (2000) Table of integrals, series, and products, 6th edn. Academic Press, San Diego
2. Hildebrand FB (1956) Introduction to numerical analysis. McGraw-Hill, New York
3. Livesley RK (1975) Matrix methods of structural analysis. Pergamon Press, Oxford
5. Ralston A, Rabinowitz P (1978) A first course in numerical analysis. McGraw-Hill, London
6. Timoshenko SP, Young DH (1965) Theory of structures, 2nd edn. McGraw-Hill, New YorkGoogle Scholar