Wolfram Computation Meets Knowledge

Wolfram Summer School


Shailesh Divey

Summer School

Class of 2013


Shailesh is a PhD candidate in Aerospace Engineering at the University of Texas at Arlington, with active research interests in Electric Helicopters and Autonomously-Healing Composite Materials. He aims to use his research to determine the commercial viability and feasibility of Electric and Hybrid-Electric Helicopters. He also holds an M.S. in Materials Science and Engineering from the University of Texas at Arlington. Shailesh is also a hobbyist drummer and a competitive lawn tennis player. He also aspires to become a proficient programmer, and eventually use all his acquired expertise, passions, and interests to become a competent and successful entrepreneur.

Project: Topological Optimization of a Truss

Trusses are a broad category of man-made structures that are often used as stiffeners in structural configurations like bridges, cranes, roof supports, construction frameworks, etc. Trusses are complex utilitarian structures that present significant modeling difficulties. The objective of this project is to topologically optimize a statically determinate truss structure with a fixed number of members (struts) and enumerate every possible configuration that was considered to arrive at the optimal truss design. The truss will be analyzed based on the first principles of Newton’s laws of motions. In order for a truss to be stable, i.e. not fall, it must be entirely composed of triangles.

Although the statically determinate condition of m ≥ 2jr where m, j, and r are the number of truss members, number of joints, and number of reactions, respectively, is necessary, it is not sufficient for stability, since truss stability also depends on truss geometry, support conditions, and load-carrying capacity of the members.

The approach towards the problem (the workflow) involves deciding on the designing of the design constraints (e.g., material properties like Young’s modulus, material density, maximum allowable or yield stress, etc.), the topological design variables (e.g., material distribution, safety factor, etc.) and an objective function (as a function of weight, length, number of members, etc.) such that an optimal stable truss configuration can be created wherein none of the joints are out of force balance. Force balance involves satisfying the following conditions:

The truss will be further tested using the high-fidelity modeling in SystemModeler for specific loading conditions in order to validate the analytical model created using Mathematica.

Favorite Four-Color, Four State Turing Machine

Rule 3003511406769249385332