Truss structures composed of members that work exclusively in tension or in compression appear in several problems of science and engineering, e.g., in the study of the resisting mechanisms of masonry structures, as well as in the design of spider web-inspired web structures. This work generalizes previous results on the existence of cable webs that are able to support assigned sets of nodal forces under tension. We extend such a problem to the limit analysis of compression-only “strut nets” subjected to fixed and variable nodal loads. These systems provide discrete element models of masonry bodies, which lie inside the polygon/polyhedron with vertices at the points of application of the given forces (“underlying masonry structures”). It is assumed that fixed nodal forces are combined with variable forces growing proportionally to a scalar multiplier (load multiplier), and that the supporting strut net is subjected to kinematic constraints at given nodal positions.
Topology optimization of tension-only cable nets under finite deformations
Structures containing tension-only members, i.e., cables, are widely used in engineered structures (e.g., suspension and cable-stayed bridges, tents, and bicycle wheels) and are also found in nature (e.g., spider webs). We seek to use the ground structure method to obtain optimal cable network configurations. The structures are modeled using principles of nonlinear elasticity that allow for large displacements, i.e., global configuration changes, and large deformations. The material is characterized by a hyperelastic constitutive relation in which the strain energy is nonzero only when the axial stretch of a member is greater than or equal to one (i.e., tension-only behavior). We maximize the stationary potential energy of the equilibrated system, which avoids the need for an additional adjoint equation in computing the derivatives needed for the solution of the optimization problem. Several examples demonstrate the capabilities of the proposed formulation for topology optimization of cable networks. Motivated by nature, a spider web–inspired cable net is designed.
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- Award ID(s):
- 1663244
- NSF-PAR ID:
- 10170740
- Date Published:
- Journal Name:
- Structural and Multidisciplinary Optimization
- ISSN:
- 1615-147X
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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To this end, we consider an approach to partition task-execution into a primary (fast) winch-tension control and secondary (slow) reconfiguration and joint-stiffness modulation. This would enable a primary trajectory-tracking task together with secondary task-space stiffness tailoring, using system-reconfiguration and joint-stiffness modulation. In this paper, we limit our scope to feasibility-evaluation to achieve the stiffness modulation as a secondary goal within an offline design-optimization setting (but with an eye towards real-time implementation).
These aspects are illustrated in the context of a 3-PRP m-CDPM for tracking a desired trajectory within its wrench-feasible workspace. The secondary-task is the directional-alignment and shaping of the stiffness ellipsoid to shape the disturbance-rejection characteristics along the trajectory. The optimization is solved through constrained minimization of a multi-objective weighted cost function subject to non-linear workspace feasibility, and inequality stiffness and tension constraints.
- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1007/s00158-020-02513-7
