ISSN:
1573-2878
Keywords:
Unilateral contact
;
structural optimization
;
truss topology design
;
maximum stiffness
;
constant contact force distribution
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract This work extends the ground structure approach of truss topology optimization to include unilateral contact conditions. The traditional design objective of finding the stiffest truss among those of equal volume is combined with a second objective of achieving a uniform contact force distribution. Design variables are the volume of bars and the gaps between potential contact nodes and rigid obstacles. The problem can be viewed as that of finding a saddle point of the equilibrium potential energy function (a convex problem) or as that of minimizing the external work among all trusses that exhibit a uniform contact force distribution (a nonconvex problem). These two formulations are related, although not completely equivalent: they give the same design, but concerning the associated displacement states, the solutions of the first formulation are included among those of the second but the opposite does not necessarily hold. In the classical noncontact single-load case problem, it is known that an optimal truss can be found by solving a linear programming (LP) limit design problem, where compatibility conditions are not taken into account. This result is extended to include unilateral contact and the second objective of obtaining a uniform contact force distribution. The LP formulation is our vehicle for proving existence of an optimal design: by standard LP theory, we need only to show primal and dual feasibility; the primal one is obvious, and the dual one is shown by the Farkas lemma to be equivalent to a condition on the direction of the external load. This method of proof extends results in the classical noncontact case to structures that have a singular stiffness matrix for all designs, including a case with no prescribed nodal displacements. Numerical solutions are also obtained by using the LP formulation. It is applied to two bridge-type structures, and trusses that are optimal in the above sense are obtained.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF02192039
Permalink
