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Finding Displacements Using Castigliano’s Theorem, LaGrange Multipliers, Heaviside Step Functions, and Numerical Integration

Citation

Gallegos, Selso. (2020-05). Finding Displacements Using Castigliano’s Theorem, LaGrange Multipliers, Heaviside Step Functions, and Numerical Integration. Theses and Dissertations Collection, University of Idaho Library Digital Collections. https://www.lib.uidaho.edu/digital/etd/items/gallegos_idaho_0089n_11854.html

Title:
Finding Displacements Using Castigliano’s Theorem, LaGrange Multipliers, Heaviside Step Functions, and Numerical Integration
Author:
Gallegos, Selso
Date:
2020-05
Keywords:
Castigliano Displacements
Program:
Mechanical Engineering
Subject Category:
Mechanical engineering; Mechanics; Engineering
Abstract:

Engineering fundamentals implemented in advanced computational programs drive innovative and precise engineering solutions in modern industrial systems. This thesis presents a practical design tool created for industrial implementation. The Generalized Form of Castigliano’s Theorem is utilized to perform an analysis determining the stress and deflection of flatbed semi-truck trailers. The solution is implemented into computer software, a graphical user interface allows design engineers to use the tool immediately after installation. The tool generates a 3-D model and a design report for assessment and documentation. The numerical solution is validated by comparing analysis results with experimental data collected in the field, concluding that the solution is indeed valid. In addition, this thesis presents a resource guide outlining examples of how to apply the theorem to essentially any mechanical problem. Castigliano’s Theorem is used to relate a point loads to displacements, it’s practical in determining the deflection in structures. The value in this thesis lies in the demonstrated practical application and the guide focused on making The Generalized Form of Castigliano’s Theorem more accessible to engineers around the world.

Description:
masters, M.S., Mechanical Engineering -- University of Idaho - College of Graduate Studies, 2020-05
Major Professor:
Odom, Edwin
Committee:
Beyerlein, Steven; Nielson, Richard J
Defense Date:
2020-05
Identifier:
Gallegos_idaho_0089N_11854
Type:
Text
Format Original:
PDF
Format:
application/pdf

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