Date of Award
8-2024
Document Type
Dissertation
Degree Name
Doctor of Philosophy (PhD)
Department
Mechanical Engineering
Committee Chair/Advisor
Dr. Gang Li
Committee Member
Dr. Georges Fadel
Committee Member
Dr. Huijuan Zhao
Committee Member
Dr. Oliver Myers
Committee Member
Dr. Vincent Blouin
Abstract
Topology optimization (TO) is an engineering design discipline dedicated to optimizing material distribution within a given domain. In traditional gradient-based topology optimization, the solid domain is discretized into small volumetric elements. Using finite element analysis (FEA) of the structure, the gradient of the objective function with respect to the design variables (the pseudo densities) is computed, and these design variables are updated iteratively until convergence is achieved. Although gradient-based TO methods are well-established, sensitivity analyses of objective functions and constraints can be both mathematically complex and computationally intensive. The nonconvex nature of most TO problems often complicates efficient convergence. Furthermore, traditional TO methods are limited in their ability to design structures that achieve specified nonlinear deformation behaviors; specifically, they struggle to match load-by-load deformations to consistently produce a topology that delivers the desired nonlinear load-deformation characteristics. In this work, with the observation that topology-optimized structures frequently resemble sparsely arranged beams, we propose to replace the initial domain of solid elements with a sparse network of morphing beam elements to largely reduce the computational cost while retaining the result fidelity. Although the substitution of solid elements with beam elements has been explored in existing literature, previous methods typically face challenges related to scalability, manufacturability, and design space limitations. More importantly, no prior efforts have focused on developing a beam network-based topology optimization method specifically aimed at achieving targeted nonlinear deformation responses, despite its potential engineering benefits. This work introduces an efficient approach to creating topology-optimized structures using a morphing beam network, thereby reducing the associated degrees of freedom and computational costs. This method can be leveraged to address more complex topology optimization problems, such as optimization for nonlinear deformation. Two types of optimization problems are examined using the proposed approach. First, to validate the method's ability to maintain the result fidelity found in gradient-based topology optimization with solid elements, we conduct an in-depth investigation of compliance minimization and compare the optimized structures with those obtained using solid elements. The second optimization investigation employs a nonlinear beam theory and leverages the efficiency of a sparse morphing beam network to generate structures with specified nonlinear load-displacement curves. Numerical results demonstrate that, by optimizing the nodal locations and beam widths in a sparse network of discretized beams, both linear and nonlinear topology-optimized structures can be produced with significantly reduced degrees of freedom and computational cost compared to traditional methods.
Recommended Citation
Montalbano, Andrew S., "Linear and Nonlinear Topology Optimization with Morphing Beam Networks" (2024). All Dissertations. 3729.
https://open.clemson.edu/all_dissertations/3729
Author ORCID Identifier
0000-0002-1179-4729