Charles L. Penninger

Implicit Uncertainty Propagation for Robust Collaborative Optimization

In this research we develop a mathematical construct for estimating uncertainties within the bilevel optimization framework of collaborative optimization. The collaborative optimization strategy employs decomposition techniques that decouple analysis tools in order to facilitate disciplinary autonomy and parallel execution. To ensure consistency of the physical artifact being designed, interdisciplinary consistency constraints are introduced at the system level. These constraints implicitly enforce multidisciplinary consistency when satisfied. The decomposition employed in collaborative optimization prevents the use of explicit propagation techniques for estimating uncertainties of system performance. In this investigation we develop and evaluate an implicit method for estimating system performance uncertainties within the collaborative optimization framework. The methodology accounts for both the uncertainty associated with design inputs and the uncertainty of performance predictions from other disciplinary simulation tools. These implicit uncertainty estimates are used as the basis for a new robust collaborative optimization (RCO) framework. The bilevel robust optimization strategy developed in this research provides for disciplinary autonomy in system design, while simultaneously accounting for performance uncertainties to ensure feasible robustness of the resulting system. The method is effective in locating a feasible robust optima in application studies involving a multidisciplinary aircraft concept sizing problem. The system-level consistency constraint formulation used in this investigation avoids the computational difficulties normally associated with convergence in collaborative optimization. The consistency constraints are formulated to have the inherent properties necessary for convergence of

Topology Synthesis of Extrusion-Based Nonlinear Transient Designs

Many practical structural designs require that the structure is easily manufactured. Design concepts synthesized using conventional topology optimization methods are typically not easily manufactured, in that multiple finishing processes are required to construct the component. A manufacturing technique that requires only minimal effort is extrusion. Extrusion is a manufacturing process used to create objects of a fixed cross-sectional profile. The result of using this process is lower costs for the manufacture of the final product. In this paper, a hybrid cellular automaton algorithm is developed to synthesize constant cross section structures that are subjected to nonlinear transient loading. The novelty of the proposed method is the ability to generate constant cross section topologies for plastic-dynamic problems since the issue of complex gradients can be avoided. This methodology is applied to extrusions with a curved sweep along the direction of extrusion as well. Three-dimensional examples are presented to demonstrate the efficiency of the proposed methodology in synthesizing these structures. Both static and dynamic loading cases are studied.

Strain-based topology optimisation for crashworthiness using hybrid cellular automata

Structural design for crashworthiness is a challenging area of research due to large plastic deformations and complex interactions among diverse components of the vehicle. Previous research in this field primarily focused on energy absorbing structures that utilise a desired amount of material. These structures have been shown to absorb a large amount of the kinetic energy generated during the crash event; however, the large plastic strains experienced can lead to material failure and loss of structural integrity. This research introduces a strain-based, dynamical multi-domain topology optimisation algorithm for crashworthy structures undergoing large deformations. This technique makes use of the hybrid cellular automaton framework, which combines transient, non-linear finite-element analysis and local control rules acting on cells. The set of all cells defines the design domain. In the proposed algorithm, the design domain is dynamically divided into two sub-domains for different objectives, i.e., high-strain sub-domain (HSSD) and low-strain sub-domain (LSSD). The distribution of these sub-domains is determined by a plastic strain limit value. During the design process, the material is distributed within the LSSD to distribute internal energy uniformly. In the HSSD, the material is distributed to satisfy a failure criterion given by a maximum strain value. Results show that the new formulation and algorithm are suitable for practical applications. The case study presented demonstrates the potential significance of this work for a wide range of engineering design problems.

A Fully Anisotropic Hierarchical Hybrid Cellular Automata Methodology to Simulate Bone Remodeling

accommodate the hierarchical structure of bone. This hierarchical-HCA methodology utilizes communication between continuum level and tissue level models of bone to guide the remodeling process. The HCA algorithm utilizes the average apparent density of the tissue level structures to update the stiffness characteristics of the continuum model of bone. In this research, a method for calculating the local anisotropic properties of these structures is developed. This approach utilizes confined uni-axial strain tests, on each tissue level model, to numerically determine the structures stiffness tensor. The objective of this work is to increase the fidelity and versatility of the hierarchical-HCA algorithm by assimilating the computed mechanical properties of the tissue level models. Preliminary analyses display improved efficiency and a more consistent material distribution when incorporating the anisotropic properties into this methodology.

Strain-Based Topology Optimization for Crashworthiness Using Hybrid Cellular Automata

Structural design for crashworthiness is a challenging area of research due to large plastic deformations and complex interactions among diverse components of the vehicle. Previous research in this field primarily focused on energy absorbing structures that utilize a desired amount of material. These structures have been shown to absorb a large amount of the kinetic energy generated during the crash event; however, the large plastic strains experienced can lead to failure. This research introduces a new strain-based topology optimization algorithm for crash-worthy structures undergoing large deformations. This technique makes use of the hybrid cellular automaton framework combining transient, non-linear finite-element analysis and local control rules acting on cells. The set of all cells defines the design domain. In the proposed algorithm, the design domain is dynamically divided into two sub-domains for different objectives, i.e., high strain sub-domain (HSSD) and low strain sub-domain (LSSD). The distribution of these sub-domains is determined by a plastic strain limit value. During the design process, the material is distributed within the LSSD following a fully-internal-energy-distribution principle. To accomplish that, each cell in the LSSD is driven to a prescribed target or set point value by modifying its stiffness. In the HSSD, the material is distributed to satisfy a failure criterion given by a maximum strain value. Results show that the new formulation and algorithm are suitable for practical applications. The case studies demonstrate the potential significance of the new capability developed for a wide range of engineering design problems.© 2009 ASME

High Fidelity Computational Model of Bone Remodeling Cellular Mechanisms

One of the most intriguing aspects of bone is its ability to grow, repair damage, adapt to mechanical loads, and maintain mineral homeostasis [1]. It is generally accepted that bone adaptation occurs in response to the mechanical demands of our daily activities; moreover, strain and microdamage have been implicated as potential stimuli that regulate bone remodeling [2]. Computational models have been used to simulate remodeling in an attempt to better understand the metabolic activities which possess the key information of how this process is carried out [3]. At present, the connection between the cellular activity of remodeling and the applied mechanical stimuli is not fully understood. Only a few mathematical models have been formulated to characterize the remolding process in terms of the cellular mechanisms that occur [4,5].Copyright

Signaling Pathways for Bone Resorption Predicted as a Hybrid Cellular Automaton Process

The bone remodeling process provides for various functions such as mineral homeostasis, damage repair, and adaptation to mechanical loading. At present, a clear link between the mechanical stimulation of bones and the biochemical response is not fully understood. Computational simulations can provide a means to test hypotheses and gain insight into processes that are difficult to examine experimentally. The objective of this work is to predict the effect of damage and strain as the stimulus for regulating the cellular signaling activity of remodeling. In this study, potential signaling pathways that mediate this cellular activity were incorporated in a hybrid cellular automaton (HCA) algorithm. Biological rules were implemented in this model to control recruitment, differentiation, and activation of osteoclasts. Prominent processes for describing recruitment and inhibition of the bone cells, as reported from experimental studies, are utilized. This work focuses on the resorption of a damaged site on a trabecular strut.© 2010 ASME

Investigation of Osteoclast Resorption Mechanisms in a Hybrid Cellular Automaton Model of Bone Remodeling

Bone is a living tissue which is continually adapting to its biological environment via continuous formation and resorption. It is generally accepted that bone remodeling occurs in response to daily mechanical loading. The remodeling process enables various functions, such as damage repair, adaptation to mechanical loads, and mineral homeostasis [1]. The cells that are responsible for the bone remodeling process are the bone resorbing osteoclasts and the bone forming osteoblasts. These cells closely coordinate their actions in a basic multicellular unit to renew “packets” of bone.© 2007 ASME