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

1Corresponding author.

ASME 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 trade off 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 piece-wise 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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