Abstract

The problem of moving a commodity with a given initial mass distribution to a pre-specified target mass distribution so that the total work is minimized can be traced back at least to Monge’s work from 1781. Here, we consider a version of this problem aiming to minimize a combination of road construction and transportation cost by determining, at each point, the local direction of transportation. This paper covers the modeling of the problem, highlights how it can be formulated as a material distribution topology optimization problem, and shows some results.

Highlights

  • Introduction and backgroundTransportation problems have a long history in science

  • This paper covers the modeling of the problem, highlights how it can be formulated as a material distribution topology optimization problem, and shows some results

  • The contribution closest in style to our work is that of Ryu et al (2012), who used topology optimization techniques to attack a path planning problem for a robot that moves in an environment with obstacles

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Summary

Introduction and background

Transportation problems have a long history in science. Already in 1781, Monge (1781) studied the problem of how to minimize the work required to move a commodity with a given initial mass distribution to a pre-specified target mass distribution. We aim to solve numerically a continuous transportation problem by using material distribution based topology optimization. The rationale for this is that road design is effectively a material distribution problem, and transportation is nothing but flow of matter. Large-scale material distribution problems have many millions or even billions of design variables (Aage et al 2017; Schmidt and Schulz 2011; Wadbro and Berggren 2009). For other problems, such as those with state constraints or those concerning wave propagation, the methodologies are still maturing. The contribution closest in style to our work is that of Ryu et al (2012), who used topology optimization techniques to attack a path planning problem for a robot that moves in an environment with obstacles

Problem description
Transportation of a product
Potential approach
Adding road design
Numerical treatment
Numerical experiments
Discussion
Full Text
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