Chandan Mozumder

An objective in crashworthiness design is to obtain energy-absorbing components. This task has been efficiently undertaken using the Hybrid Cellular Automaton method. This method combines the CA paradigm with nonlinear, dynamic finite element analysis. Lightweight, energy-absorbing topology concepts have been obtained with this approach. This paper furthers the development of the HCA method to an efficient tool for synthesising shell structures using topometry optimisation. The objective is to… Show more

An objective in crashworthiness design is to obtain energy-absorbing components. This task has been efficiently undertaken using the Hybrid Cellular Automaton method. This method combines the CA paradigm with nonlinear, dynamic finite element analysis. Lightweight, energy-absorbing topology concepts have been obtained with this approach. This paper furthers the development of the HCA method to an efficient tool for synthesising shell structures using topometry optimisation. The objective is to find the thickness distribution that uniformly distributes the structures internal energy density. This approach addresses problems involving collisions, large displacement and material plastic hardening. The final designs meet manufacturing and performance constraints. Show less

In reliability based design optimization, a methodology for finding optimized designs characterized with a low probability of failure the main objective is to minimize a merit function while satisfying the reliability constraints. Traditionally, these have been formulated as a double-loop (nested) optimization problem, which is computationally intensive. A new efficient unilevel formulation for reliability based design optimization was developed by the authors in earlier studies, where the… Show more

In reliability based design optimization, a methodology for finding optimized designs characterized with a low probability of failure the main objective is to minimize a merit function while satisfying the reliability constraints. Traditionally, these have been formulated as a double-loop (nested) optimization problem, which is computationally intensive. A new efficient unilevel formulation for reliability based design optimization was developed by the authors in earlier studies, where the lower-level optimization was replaced by its corresponding first-order Karush-Kuhn-Tucker (KKT) necessary optimality conditions at the upper-level optimization and imposed as equality constraints. But as most commercial optimizers are usually numerically unreliable when applied to problems accompanied by many equality constraints, an optimization framework for reliability based design using the unilevel formulation is developed here. Homotopy methods are used for constraint relaxation and to obtain a relaxed feasible design and heuristic scheme is employed to update the homotopy parameter. Show less

In this paper, a Hybrid Cellular Automaton (HCA) algorithm has been utilized to develop an efficient methodology for synthesizing structures under a dynamic loading event. This method utilizes the cellular automata computing paradigm with the nonlinear transient finite element analysis. Previous work in topology optimization for structural design has concentrated on modeling assuming static loading conditions due to the complexities associated with dynamic loading. An HCA method has been… Show more

In this paper, a Hybrid Cellular Automaton (HCA) algorithm has been utilized to develop an efficient methodology for synthesizing structures under a dynamic loading event. This method utilizes the cellular automata computing paradigm with the nonlinear transient finite element analysis. Previous work in topology optimization for structural design has concentrated on modeling assuming static loading conditions due to the complexities associated with dynamic loading. An HCA method has been developed to address more complicated cases that involve dynamic events, such as impacts and collisions. To illustrate this technology, a generic design domain that represents an automotive crush structure is presented to demonstrate the efficiency of the proposed methodology in synthesizing crashworthy, constant cross section structures. Influence of mass fraction on final topology and application of this methodology for multiple load cases is presented. Show less

Reliability-based design optimization (RBDO) is a methodology for finding optimized designs that are characterized with a low probability of failure. Primarily, RBDO consists of optimizing a merit function while satisfying reliability constraints. The reliability constraints are constraints on the probability of failure corresponding to each of the failure modes of the system or a single constraint on the system probability of failure, which is usually estimated by performing a reliability… Show more

Reliability-based design optimization (RBDO) is a methodology for finding optimized designs that are characterized with a low probability of failure. Primarily, RBDO consists of optimizing a merit function while satisfying reliability constraints. The reliability constraints are constraints on the probability of failure corresponding to each of the failure modes of the system or a single constraint on the system probability of failure, which is usually estimated by performing a reliability analysis. Traditionally, RBDO have been formulated as a double-loop optimization problem. The upper level optimization loop generally involves optimizing a merit function subject to reliability constraints, and the lower level optimization loops compute the probabilities of failure corresponding to the failure modes that govern the system failure. This formulation is computationally intensive. Researchers have provided sequential strategies to address this issue, where the deterministic optimization and reliability analysis are decoupled, and the process is performed iteratively until convergence is achieved. These methods, though attractive in terms of obtaining a workable reliable design at considerably reduced computational costs, often lead to premature convergence and yield spurious optimal designs. In this paper, a novel unilevel formulation for RBDO is developed. In this formulation, the lower level optimization (evaluation of reliability constraints in the double-loop formulation) is replaced by its corresponding first-order Karush–Kuhn–Tucker (KKT) necessary optimality conditions at the upper level optimization. Such a replacement is computationally equivalent to solving the original nested optimization if the lower level optimization problem is solved by numerically satisfying the KKT conditions. It is shown through the use of test problems that the proposed formulation is numerically robust and computationally efficient compared to the existing approaches for RBDO. Show less