Research Papers

Conceptual Design of Structures Using an Upper Bound of von Mises Stress

[+] Author and Article Information
Ashok V. Kumar

Department of Mechanical and
Aerospace Engineering,
University of Florida,
Gainesville, FL 32611
e-mail: akumar@ufl.edu

Contributed by the Computers and Information Division of ASME for publication in the JOURNAL OF COMPUTING AND INFORMATION SCIENCE IN ENGINEERING. Manuscript received March 26, 2018; final manuscript received September 30, 2018; published online November 19, 2018. Assoc. Editor: Krishnan Suresh.

J. Comput. Inf. Sci. Eng 19(1), 011005 (Nov 19, 2018) (13 pages) Paper No: JCISE-18-1076; doi: 10.1115/1.4041705 History: Received March 26, 2018; Revised September 30, 2018

Optimal layouts for structural design have been generated using topology optimization approach with a wide variety of objectives and constraints. Minimization of compliance is the most common objective but the resultant structures often have stress concentrations. Two new objective functions, constructed using an upper bound of von Mises stress, are presented here for computing design concepts that avoid stress concentration. The first objective function can be used to minimize mass while ensuring that the design is conservative and avoids stress concentrations. The second objective can be used to tradeoff between maximizing stiffness versus minimizing the maximum stress to avoid stress concentration. The use of the upper bound of von Mises stress is shown to avoid singularity problems associated with stress-based topology optimization. A penalty approach is used for eliminating stress concentration and stress limit violations which ensures conservative designs while avoiding the need for special algorithms for handling stress localization. In this work, shape and topology are represented using a density function with the density interpolated piecewise over the elements to obtain a continuous density field. A few widely used examples are utilized to study these objective functions.

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Fig. 1

Topology optimization results for shear loaded bracket: (a) shear load = 10 MPa and (b) shear load = 50 MPa

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Fig. 2

Convergence of mass and stress for two bar frame

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Fig. 3

Plane stress model of a loaded L-shaped structure

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Fig. 4

Topology optimization results for L-shaped structure: (a) compliance minimization, (b) von Mises stress distribution, (c) minimize mass with constraint on stress (m = 3), and (d) von Mises stress distribution

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Fig. 5

Convergence of mass and stress for L-shaped bracket

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Fig. 6

Topology convergence history

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Fig. 7

Effect of the weighting parameter α

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Fig. 8

Optimal topology versus the power of strain energy density: (a) m=1, (b) m=2, (c) m=6, and (d) m=8

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Fig. 9

Convergence of maximum von Mises stress for L-bracket

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Fig. 10

Feasible region for portal frame design

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Fig. 11

Portal Frame: minimization of mass with constraint on stress (m = 3): (a) optimal topology and (b) von Mises stress (MPa)

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Fig. 12

Portal frame: optimal topology versus the power of strain energy density: (a) m=1, (b) m=3, and (c) m=6

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Fig. 13

Convergence of mass and stress for portal frame

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Fig. 14

Convergence of maximum von Mises stress for the portal frame



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