Cellular Automata-Like Systems and Evolution of Plane Trusses

4 Cellular Automata-Like Systems and Evolution of Plane Trusses 

Two plane trusses the left is stable, the right unstable. 

Truss Stress Analysis The computation of member forces in an arbitrary plane truss is now examined. There exist some simple counting tests that may determine if a given truss is unstable. Failing that, one must attempt to compute the equilibrium state given some external forces in the process, one obtains values for all member forces. In this example, all truss members are identical in terms of material and area, grown in a developmental space where units are measured in meters EA is set to 1.57 x 104 N, corresponding to a modulus of elasticity for steel and a cylindrical member of diameter 1 cm. Consider a general truss with n joints and m beams external forces are applied at joints and the member forces are computed. Let the structure forces be 

One may relate the individual member forces to displacement and structure forces as follows  

Therefore, given a plane truss, one may first compute the stiffness matrix, then compute the displacements, then the individual member forces. The entire process is bounded by the calculation of a matrix inversion (or LU-Decomposition), and, hence, has running time 0(m3). 

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