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Systematic summary of factors which are involved in optimization of given structural configuration is part of report resulting from study of analysis of objective function. Predicted reliability of performance of finished structure is sharply dependent upon results of coupon tests. Optimization analysis developed by study also involves expected cost of proof testing.
A weight-reduction algorithm is developed for the optimal design of structures subject to several multibehavioral inequality constraints. The structural weight is considered to depend linearly on the design variables. The algorithm incorporates a simple recursion formula derived from the Kuhn-Tucker necessary conditions for optimality, associated with a procedure to delete nonactive constraints based on the Gauss-Seidel iterative method for linear systems. A number of example problems is studied, including typical truss structures and simplified wings subject to static loads and with constraints imposed on stresses and displacements. For one of the latter structures, constraints on the fundamental natural frequency and flutter speed are also imposed. The results obtained show that the method is fast, efficient, and general when compared to other competing techniques. Extensions to the generality of the method to include equality constraints and nonlinear merit functions is discussed.
The superior survivability of a multirole fighter is dependent upon balanced integration of technologies for reduced vulnerability and susceptability. The objective is to develop a methodology for structural design optimization with survivability dependent constraints. The design criteria for optimization will be survivability in a tactical laser environment. The following analyses are studied to establish a dependent design relationship between structural weight and survivability: (1) develop a physically linked global design model of survivability variables; and (2) apply conventional constraints to quantify survivability dependent design. It was not possible to develop an exact approach which would include all aspects of survivability dependent design, therefore guidelines are offered for solving similar problems.
Structural synthesis method applied to weight optimization design of two span indeterminate beam
Integrated structural analysis and design systems and structural optimization procedures are being used in a production environment. Successful use of these systems requires experienced personnel. Interactive computer graphics can and will play a significant role in the analysis, optimization, design and manufacturing areas. Practical structural optimization procedures are tools that must be made available to the team. Much work still needs to be done to tie finite-element modeling to actual design details which are being tracked on systems such as CADAM or CATIA. More work needs to be done to automate the detailed design and analysis process. More emphasis should be placed on the real design problems.
The binding of the sulfate ligand group to monovalent cations in the presence of water is important for many systems. To understand the structure and energetics of sulfate complexes, we use density functional theory to study ethyl sulfate binding to the monovalent cations Li + , Na + , and K + , and to water. The free energies of binding and optimal structures are calculated for a range of the number of ethyl sulfates and waters. Without water, the most optimal structure for all the cations is bidentate binding by two ethyl sulfates, yielding a 4-fold coordination. With water, the lowest free energy structures also have two ethyl sulfates, but the coordination varies with cations. For complexes with water, the four oxygen atoms in the sulfate group enable multiple binding geometries for the cations and for hydrogen bonding with water. Many of these geometries differ in free energy by only a small amount (1–2 kcal/mol), meaning there will be multiple binding configurations in bulk solution. In comparison to the optimal structures for binding to the carboxylate group, there is more variation for binding to the sulfate group as a function of cation type and the number of waters. Further, the polarization of the atoms is significant and varies among the sulfate oxygen atoms. The water oxygen charge is often larger than that of sulfate oxygen, which plays a role in the preference for monodentate ligand binding to cations in the presence of water.
Aerospace-industry applications of general-purpose structural optimization codes have not progressed as far as they might due to the lack of preprocessor capabilities. With the emergence of a new generation of graphic preprocessors that are capable of creating design models, these methods will gain acceptance. Attention is given to recent innovative applications of the Flutter and Strength Optimization Program and TSO, and the role of structural optimization in a multidisciplinary design system. Illustrative aircraft structure examples are used throughout the presentation.
In this study the vibration control of large space structures with structural damping is investigated. Emphasis is made on the control of both a class of optimally designed (stepped) structures and also the corresponding uniform structures using a cantilever beam as an example. The open loop and closed loop dynamics are compared and the transient responses are determined to study the effect of damping on the control system design.
A computational simulation method is presented for Non-Deterministic Multidisciplinary Optimization of engine composite materials and structures. A hypothetical engine duct made with ceramic matrix composites (CMC) is evaluated probabilistically in the presence of combined thermo-mechanical loading. The structure is tailored by quantifying the uncertainties in all relevant design variables such as fabrication, material, and loading parameters. The probabilistic sensitivities are used to select critical design variables for optimization. In this paper, two approaches for non-deterministic optimization are presented. The non-deterministic minimization of combined failure stress criterion is carried out by: (1) performing probabilistic evaluation first and then optimization and (2) performing optimization first and then probabilistic evaluation. The first approach shows that the optimization feasible region can be bounded by a set of prescribed probability limits and that the optimization follows the cumulative distribution function between those limits. The second approach shows that the optimization feasible region is bounded by 0.50 and 0.999 probabilities.
Here, the accurate mapping of potential energy surfaces (PESs) is crucial to our understanding of the numerous physical and chemical processes mediated by atomic rearrangements, such as conformational changes and chemical reactions, and the thermodynamic and kinetic feasibility of these processes. Stochastic electronic structure theories, e.g., Quantum Monte Carlo (QMC) methods, enable highly accurate total energy calculations that in principle can be used to construct the PES. However, their stochastic nature poses a challenge to the computation and use of forces and Hessians, which are typically required in algorithms for minimum-energy pathway (MEP) and transition state (TS) identification, such as the nudged elastic band (NEB) algorithm and its climbing image formulation. Here, we present strategies that utilize the surrogate Hessian line-search method, previously developed for QMC structural optimization, to efficiently identify MEP and TS structures without requiring force calculations at the level of the stochastic electronic structure theory. By modifying the surrogate Hessian algorithm to operate in path-orthogonal subspaces and at saddle points, we show that it is possible to identify MEPs and TSs by using a force-free QMC approach. We demonstrate these strategies via two examples, the inversion of the ammonia (NH 3 ) molecule and the nucleophilic substitution (S N 2) reaction F – + CH 3 F → FCH 3 + F – . We validate our results using Density Functional Theory (DFT)- and Coupled Cluster (CCSD, CCSD(T))-based NEB calculations. We then introduce a hybrid DFT-QMC approach to compute thermodynamic and kinetic quantities, free energy differences, rate constants, and equilibrium constants that incorporates stochastically optimized structures and their energies, and show that this scheme improves upon DFT accuracy. Our methods generalize straightforwardly to other systems and other high-accuracy theories that similarly face challenges computing energy gradients, paving the way for highly accurate PES mapping, transition state determination, and thermodynamic and kinetic calculations at significantly reduced computational expense.
This report covers work conducted under grant NAG1-1562 for the NASA High Performance Computing and Communications Program (HPCCP) from December 7, 1993, to December 31, 1997. The objective of the research was to develop new multidisciplinary design optimization (MDO) techniques which exploit parallel computing to reduce the computational burden of aircraft MDO. The design of the High-Speed Civil Transport (HSCT) air-craft was selected as a test case to demonstrate the utility of our MDO methods. The three major tasks of this research grant included: development of parallel multipoint approximation methods for the aerodynamic design of the HSCT, use of parallel multipoint approximation methods for structural optimization of the HSCT, mathematical and algorithmic development including support in the integration of parallel computation for items (1) and (2). These tasks have been accomplished with the development of a response surface methodology that incorporates multi-fidelity models. For the aerodynamic design we were able to optimize with up to 20 design variables using hundreds of expensive Euler analyses together with thousands of inexpensive linear theory simulations. We have thereby demonstrated the application of CFD to a large aerodynamic design problem. For the predicting structural weight we were able to combine hundreds of structural optimizations of refined finite element models with thousands of optimizations based on coarse models. Computations have been carried out on the Intel Paragon with up to 128 nodes. The parallel computation allowed us to perform combined aerodynamic-structural optimization using state of the art models of a complex aircraft configurations.
Non-linear programming algorithms play an important role in structural design optimization. Fortunately, several algorithms with computer codes are available. At NASA Lewis Research Centre, a project was initiated to assess the performance of eight different optimizers through the development of a computer code CometBoards. This paper summarizes the conclusions of that research. CometBoards was employed to solve sets of small, medium and large structural problems, using the eight different optimizers on a Cray-YMP8E/8128 computer. The reliability and efficiency of the optimizers were determined from the performance of these problems. For small problems, the performance of most of the optimizers could be considered adequate. For large problems, however, three optimizers (two sequential quadratic programming routines, DNCONG of IMSL and SQP of IDESIGN, along with Sequential Unconstrained Minimizations Technique SUMT) outperformed others. At optimum, most optimizers captured an identical number of active displacement and frequency constraints but the number of active stress constraints differed among the optimizers. This discrepancy can be attributed to singularity conditions in the optimization and the alleviation of this discrepancy can improve the efficiency of optimizers.
The development of novel composite mechanics for the analysis of damping in composite laminates and structures and the more significant results of this effort are summarized. Laminate mechanics based on piecewise continuous in-plane displacement fields are described that can represent both intralaminar stresses and interlaminar shear stresses and the associated effects on the stiffness and damping characteristics of a composite laminate. Among other features, the mechanics can accurately model the static and damped dynamic response of either thin or thick composite laminates, as well as, specialty laminates with embedded compliant damping layers. The discrete laminate damping theory is further incorporated into structural analysis methods. In this context, an exact semi-analytical method for the simulation of the damped dynamic response of composite plates was developed. A finite element based method and a specialty four-node plate element were also developed for the analysis of composite structures of variable shape and boundary conditions. Numerous evaluations and applications demonstrate the quality and superiority of the mechanics in predicting the damped dynamic characteristics of composite structures. Finally, additional development was focused on the development of optimal tailoring methods for the design of thick composite structures based on the developed analytical capability. Applications on composite plates illustrated the influence of composite mechanics in the optimal design of composites and the potential for significant deviations in the resultant designs when more simplified (classical) laminate theories are used.
In this talk we shall discuss algorithms and CAD tools for the design and analysis of structures for high performance applications using advanced composite materials. An extensive mathematical theory for optimal structural (e.g., shape) design was developed over the past thirty years. Aspects of this theory have been used in the design of components for hypersonic vehicles and thermal diffusion systems based on homogeneous materials. Enhancement of the design methods to include optimization of the microstructure of the component is a significant innovation which can lead to major enhancements in component performance. Our work is focused on the adaptation of existing theories of optimal structural design (e.g., optimal shape design) to treat the design of structures using advanced composite materials (e.g., fiber reinforced, resin matrix materials). In this talk we shall discuss models and algorithms for the design of simple structures from composite materials, focussing on a problem in thermal management. We shall also discuss methods for the integration of active structural controls into the design process.
ROCOPT is a user-friendly, graphically-interfaced, microcomputer-based computer program (IBM compatible) that optimizes rocket components by minimizing the structural weight. The rocket components considered are ring stiffened truncated cones and cylinders. The applied loading is static, and can consist of any combination of internal or external pressure, axial force, bending moment, and torque. Stress margins are calculated by means of simple closed form strength of material type equations. Stability margins are determined by approximate, orthotropic-shell, closed-form equations. A modified form of Powell's method, in conjunction with a modified form of the external penalty method, is used to determine the minimum weight of the structure subject to stress and stability margin constraints, as well as user input constraints on the structural dimensions. The graphical interface guides the user through the required data prompts, explains program options and graphically displays results for easy interpretation.
Designing an energy absorber for automotive bumpers involves balancing low-speed and high-speed impacts to ensure safety, reduce repair costs, and meet regulatory standards. Here, this study explores a novel design using multi-material 3D printing and structural optimization to fabricate a lightweight and cost-efficient energy absorber. The design effectively dissipates energy in low-speed collisions and minimizes force transmission in high-speed pedestrain impacts, helping to meet both safety and performance requirements. The energy absorber design combines 20% carbon fiber-reinforced acrylonitrile butadiene styrene (CF-ABS) and thermoplastic polyurethane (TPU) for optimal stiffness and flexibility. It uses 3D-printed lattice structures optimized through finite element simulations to help meet both low-speed and high-speed impact requirements. Full-scale energy absorbers were 3D-printed using optimized CF-ABS/TPU blends and tested under high-speed impact using the Flexible Pedestrian Legform Impactor (Flex-PLI). For fair comparison, a baseline bumper with a traditional triangular lattice structure, also 3D-printed from the same CF-ABS/TPU materials, was similarly tested. Interestingly, both the optimized and baseline 3D-printed energy absorbers showed nearly identical performance, successfully meeting injury limits. Their performances were also benchmarked against an injection-molded energy absorber. While both 3D-printed and injection-molded designs met injury limits, the 3D-printed absorber exhibited a higher tibia bending moment, indicating an opportunity for further optimization. A Techno-Economic Analysis compared the costs of producing energy absorbers using traditional manufacturing and 3D printing. The analysis highlighted that 3D printing offers cost benefits for low to medium production volumes, with the total cost per energy absorber at ∼ $\$$74, compared to traditional methods that become economical beyond 2000 units.
The rational use of optimality criteria was investigated for a class of structural synthesis problems where materials, configuration and applied load conditions are specified, and the minimum weight design is to be determined. The potential of hybrid methods of structural optimization for dealing with relatively large design problems involving practical complexity was explored. The reduced basis concept in design space was used to decrease the number of generalized design variables dealt with by the mathematical programming algorithm. Optimality criteria methods for obtaining design vectors associated with displacement, system buckling and natural frequency constraints are presented. A stress ratio method was used to generate a basis design vector representing the stress constraints. The finite element displacement method was used as the basic structural analysis tool. Results for several examples of truss systems subject to stress, displacement and minimum size constraints are presented. An assessment of these results indicates the effectiveness of the hybrid method developed.
In this paper the design of an active control law for the rejection of persistent disturbances in large space structures is presented. The control system design approach is based on a deterministic model of the disturbances, with a model-based-compensator (MBC) structure, optimizing the magnitude of the disturbance that the structure can tolerate without violating certain predetermined constraints. In addition to closed-loop stability, the explicit treatment of state, control and control rate constraints, such as structural displacement, control actuator effort, and compensator time guarantees that the final design will exhibit desired performance characteristics. The technique is applied for the vibration damping of a simple two bay truss structure which is subjected to persistent disturbances, such as shuttle docking. Preliminary results indicate that the proposed control system can reject considerable persistent disturbances by utilizing most of the available control, while limiting the structural displacements to within desired tolerances. Further work, however, for incorporating additional design criteria, such as compensator robustness to be traded-off against performance specifications, is warranted.