Simulationsmethoden im textilen Leichtbau – Die Entwicklung seit 1972 und aktueller Stand

Abstract

ESSAY

A form-finding method for adaptive truss structures subject to multiple static load cases

“…However, for the collective of the load cases, one obtains an optimized form, actuation, and prestressing. Along with (21), the problem statement (15)…”

“…In the remainder, the external force loads are assumed to be constant. Thus, the load factors in O O  n n j do not serve as unknowns and the number of unknowns in (15)…”

“…Under the assumptions described, the form-finding problem (15) can be solved by means of an iterative scheme, presuming a mechanically reasonable formulation. Figure 11 shows the structural layout of the Jacobian matrix J (size n n eq var × ), which occurs in the linearization of (15). While the derivatives of the equilibrium equations and design constraints in each individual load case are independent of other load cases, the inter-configurational compatibility constraints (19) couple the equations for each load case j > 1 with load case j = 1.…”

“…Finally, the individual equilibrium states have to be investigated due to stability using appropriate methods. As the elastic properties of the passive elements are included in the form-finding problem (15), one may think of considering stability aspects already during form-finding. However, this is out of the scope of this article.…”

“…with the external loads 34), (35), and (36) form a well-posed system of nonlinear equations (15). The initial values for the unknowns (iteration step k = 0) are assumed as in the previous case.…”