Reliability-based Topology Optimization of Trusses with Stochastic Stiffness

A new method is proposed for reliability-based topology optimization of truss structures with random geometric imperfections and material variability. Such imperfections and variability, which may result from manufacturing processes, are assumed to be small in relation to the truss dimensions and mean material properties and normally distributed. Extensive numerical evidence suggests that the trusses, when optimized in terms of a displacement-based demand metric, are characterized by randomness in the stiffness that follow the Gumbel distribution. Based on this observation, it was possible to derive analytical expressions for the structural reliability, enabling the formulation of a computationally efficient single-loop reliability-based topology optimization algorithm. Response statistics are estimated using a second-order perturbation expansion of the stiffness matrix and design sensitivities are derived so that they can be directly used by gradient-based optimizers. Several examples illustrate the accuracy of the perturbation expressions and the applicability of the method for developing optimal designs that meet target reliabilities

Optimal Design of Trusses With Geometric Imperfections

The present paper focuses on optimization of trusses that have randomness in geometry that may arise from fabrication errors. The analysis herein is a generalization of a perturbation approach to topology optimization under geometric uncertainties. The main novelty in the present paper is in the consideration of potential buckling due to misaligned structural members. The paper begins with a brief review of the aforementioned perturbation approach, then proceeds with the analysis of the nonlinear effects of geometric imperfection. The paper concludes with some numerical examples

Optimal Design of Trusses With Geometric Imperfections: Accounting for Global Instability

A topology optimization method is proposed for the design of trusses with random geometric imperfections due to fabrication errors. This method is a generalization of a previously developed perturbation approach to topology optimization under geometric uncertainties. The main novelty in the present paper is that the objective function includes the nonlinear effects of potential buckling due to misaligned structural members. Solutions are therefore dependent on the magnitude of applied loads and the direction of resulting internal member forces (whether they are compression or tension). Direct differentiation is used in the sensitivity analysis, and analytical expressions for the associated derivatives are derived in a form that is computationally efficient. A series of examples illustrate how the effects of geometric imperfections and buckling may have substantial influence on truss design. Monte Carlo simulation together with second-order elastic analysis is used to verify that solutions offer improved performance in the presence of geometric uncertainties

Structural Topology Optimization: Moving Beyond Linear Elastic Design Objectives

Topology optimization is a systematic, free-form approach to the design of structures. It simultaneously optimizes material quantities and system connectivity, enabling the discovery of new, high-performance structural concepts. While powerful, this design freedom has a tendency to produce solutions that are unrealizable or impractical from a structural engineering perspective. Examples include overly complex topologies that are expensive to construct and ultra-slender subsystems that may be overly susceptible to imperfections. This paper summarizes recent tools developed by the authors capable of mitigating these shortcomings through consideration of (1) constructability, (2) nonlinear mechanics, and (3) uncertainties

Interfacing Building Response with Human Behavior Under Seismic Events

The goal of this paper is to model the interaction of humans with their built environment during and immediately following a natural disaster. The study uses finite element simulations to evaluate the response of buildings under input ground motions and agent-based dynamic modeling to model the subsequent evacuation of building occupants in the study area immediately following the seismic event. The structural model directly captures building damage and collapse, as well as floor accelerations and displacements to determine nonstructural damage, injuries and fatalities. The goal of this research is to make connections between building damage and occupant injuries, with geographic automata as the information handler for the agent-based platform. This research demonstrates that human behavior and evacuation patterns can be evaluated in the context of realistic structural and nonstructural damage assessments, and that prior knowledge of evacuation patterns is critical for adequate preparedness of cities to severe earthquakes

Interfacing Building Response with Human Behavior Under Seismic Events

The goal of this paper is to model the interaction of humans with their built environment during and immediately following a natural disaster. The study uses finite element simulations to evaluate the response of buildings under input ground motions and agent-based dynamic modeling to model the subsequent evacuation of building occupants in the study area immediately following the seismic event. The structural model directly captures building damage and collapse, as well as floor accelerations and displacements to determine nonstructural damage, injuries and fatalities. The goal of this research is to make connections between building damage and occupant injuries, with geographic automata as the information handler for the agent-based platform. This research demonstrates that human behavior and evacuation patterns can be evaluated in the context of realistic structural and nonstructural damage assessments, and that prior knowledge of evacuation patterns is critical for adequate preparedness of cities to severe earthquakes

Reliability-based Topology Optimization of Trusses with Stochastic Stiffness

A new method is proposed for reliability-based topology optimization of truss structures with random geometric imperfections and material variability. Such imperfections and variability, which may result from manufacturing processes, are assumed to be small in relation to the truss dimensions and mean material properties and normally distributed. Extensive numerical evidence suggests that the trusses, when optimized in terms of a displacement-based demand metric, are characterized by randomness in the stiffness that follow the Gumbel distribution. Based on this observation, it was possible to derive analytical expressions for the structural reliability, enabling the formulation of a computationally efficient single-loop reliability-based topology optimization algorithm. Response statistics are estimated using a second-order perturbation expansion of the stiffness matrix and design sensitivities are derived so that they can be directly used by gradient-based optimizers. Several examples illustrate the accuracy of the perturbation expressions and the applicability of the method for developing optimal designs that meet target reliabilities

Optimal Design of Trusses With Geometric Imperfections

The present paper focuses on optimization of trusses that have randomness in geometry that may arise from fabrication errors. The analysis herein is a generalization of a perturbation approach to topology optimization under geometric uncertainties. The main novelty in the present paper is in the consideration of potential buckling due to misaligned structural members. The paper begins with a brief review of the aforementioned perturbation approach, then proceeds with the analysis of the nonlinear effects of geometric imperfection. The paper concludes with some numerical examples

Mechanical and Electrical Characterization of Entangled Networks of Carbon Nanofibers

Entangled networks of carbon nanofibers are characterized both mechanically and electrically. Results for both tensile and compressive loadings of the entangled networks are presented for various densities. Mechanically, the nanofiber ensembles follow the micromechanical model originally proposed by van Wyk nearly 70 years ago. Interpretations are given on the mechanisms occurring during loading and unloading of the carbon nanofiber components