A Variable-Topology Morphing Composite Cylindrical Lattice

Abstract This paper describes a new method for variable-topology shape optimization. The method addresses certain problems that arise in relaxed formulations (i.e., homogenization design methods). For example, a complete relaxation generates optimal designs containing material with perforated microstructures that may be difficult or expensive to manufacture. Formulations that penalize perforated material, either explicitly or through a partial relaxation, can generate manufacturable designs. However, the same illposedness that motivates relaxed formulations reappears as the penalty against perforated material is strengthened. The practical consequence is that numerical implementations of the penalized formulations fail to converge with grid refinement. The new approach uses a control on the design perimeter to effectively exclude chattering designs (which have an infinite perimeter) from the feasible solution space. This achieves a well-posed shape design problem without the introduction of microstructure. Numerical examples demonstrate that manufacturable designs can be obtained in a single, automatic operation. Grid refinement improves geometric resolution without altering the design topology. The new method also provides a means to control the number and the length scale of holes in the optimal design.

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BASIC PROBLEMS OF THE THEORY FOR THE VARIABLE TOPOLOGY MECHANISMS

Journal of Mechanical Engineering ◽

10.3901/jme.2005.08.056 ◽

2005 ◽

Vol 41 (08) ◽

pp. 56 ◽

Cited By ~ 6

Author(s):

Chuanhe Liu

Keyword(s):

Variable Topology

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Three-Position Rigid Body Guidance Using Specified Moving Pivots for a Four-Bar Mechanism With Variable Topology

Volume 5A: 42nd Mechanisms and Robotics Conference ◽

10.1115/detc2018-85984 ◽

2018 ◽

Author(s):

Brian J. Slaboch

Keyword(s):

Rigid Body ◽

Algebraic Solution ◽

Graphical Approach ◽

Practical Applications ◽

Joint Geometry ◽

Topological State ◽

Variable Topology

This paper provides an algorithm allowing a designer to perform three position rigid body guidance with specified moving pivots for a 4R-RRRP mechanism with variable topology (MVT). A mechanism with variable topology is a mechanism that changes from one topological state to another due to a change in joint geometry. Both a graphical approach and an algebraic solution are presented. An example is provided in which a circuit defect in a 4R mechanism can be avoided using a 4R-RRRP mechanism. Two additional examples are provided that show the results of this new theory. Practical applications for this theory are found in many industries including manufacturing, aerospace, and healthcare.

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