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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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A Real-Time Algorithm for Computing the Tension Force in a Suspended Elastic Sagging Cable
An algorithm is presented for computing the tension in an elastic cable subject to sagging under its own weight, a problem highly relevant in tethered systems such as cable-driven parallel robots. This requires solving the two coupled equations of the Irvine cable model, which give the endpoint position as a function of vertical and horizontal components of tension. Via a change of variables, we reformulate this system as a pair of uncoupled equations, which are shown to have a unique solution. We develop an efficient numerical procedure to solve one of these, after which closed-form formulas provide the solution of the second equation and ultimately the tension components.
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- Award ID(s):
- 2144732
- PAR ID:
- 10562618
- Editor(s):
- Larochelle, Pierre; McCarthy, J Michael; Lusk, Craig P
- Publisher / Repository:
- Springer
- Date Published:
- ISBN:
- 978-3-031-60617-5
- Page Range / eLocation ID:
- 179-187
- Format(s):
- Medium: X
- Location:
- St. Petersburg, Florida
- Sponsoring Org:
- National Science Foundation
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