Optimization Testbed Cometboards Extended into Stochastic Domain

COMparative Evaluation Testbed of Optimization and Analysis Routines for the Design of Structures (CometBoards) is a multidisciplinary design optimization software. It was originally developed for deterministic calculation. It has now been extended into the stochastic domain for structural design problems. For deterministic problems, CometBoards is introduced through its subproblem solution strategy as well as the approximation concept in optimization. In the stochastic domain, a design is formulated as a function of the risk or reliability. Optimum solution including the weight of a structure, is also obtained as a function of reliability. Weight versus reliability traced out an inverted-S-shaped graph. The center of the graph corresponded to 50 percent probability of success, or one failure in two samples. A heavy design with weight approaching infinity could be produced for a near-zero rate of failure that corresponded to unity for reliability. Weight can be reduced to a small value for the most failure-prone design with a compromised reliability approaching zero. The stochastic design optimization (SDO) capability for an industrial problem was obtained by combining three codes: MSC/Nastran code was the deterministic analysis tool, fast probabilistic integrator, or the FPI module of the NESSUS software, was the probabilistic calculator, and CometBoards became the optimizer. The SDO capability requires a finite element structural model, a material model, a load model, and a design model. The stochastic optimization concept is illustrated considering an academic example and a real-life airframe component made of metallic and composite materials

Integrated force method versus displacement method for finite element analysis

A novel formulation termed the integrated force method (IFM) has been developed in recent years for analyzing structures. In this method all the internal forces are taken as independent variables, and the system equilibrium equations (EE's) are integrated with the global compatibility conditions (CC's) to form the governing set of equations. In IFM the CC's are obtained from the strain formulation of St. Venant, and no choices of redundant load systems have to be made, in constrast to the standard force method (SFM). This property of IFM allows the generation of the governing equation to be automated straightforwardly, as it is in the popular stiffness method (SM). In this report IFM and SM are compared relative to the structure of their respective equations, their conditioning, required solution methods, overall computational requirements, and convergence properties as these factors influence the accuracy of the results. Overall, this new version of the force method produces more accurate results than the stiffness method for comparable computational cost

Compatibility conditions of structural mechanics for finite element analysis

The equilibrium equations and the compatibility conditions are fundamental to the analyses of structures. However, anyone who undertakes even a cursory generic study of the compatibility conditions can discover, with little effort, that historically this facet of structural mechanics had not been adequately researched by the profession. Now the compatibility conditions (CC's) have been researched and are understood to a great extent. For finite element discretizations, the CC's are banded and can be divided into three distinct categories: (1) the interface CC's; (2) the cluster or field CC's; and (3) the external CC's. The generation of CC's requires the separating of a local region, then writing the deformation displacement relation (ddr) for the region, and finally, the eliminating of the displacements from the ddr. The procedure to generate all three types of CC's is presented and illustrated through examples of finite element models. The uniqueness of the CC's thus generated is shown

Completed Beltrami-Michell Formulation in Polar Coordinates

A set of conditions had not been formulated on the boundary of an elastic continuum since the time of Saint-Venant. This limitation prevented the formulation of a direct stress calculation method in elasticity for a continuum with a displacement boundary condition. The missed condition, referred to as the boundary compatibility condition, is now formulated in polar coordinates. The augmentation of the new condition completes the Beltrami-Michell formulation in polar coordinates. The completed formulation that includes equilibrium equations and a compatibility condition in the field as well as the traction and boundary compatibility condition is derived from the stationary condition of the variational functional of the integrated force method. The new method is illustrated by solving an example of a mixed boundary value problem for mechanical as well as thermal loads

Neural Network and Regression Soft Model Extended for PAX-300 Aircraft Engine

In fiscal year 2001, the neural network and regression capabilities of NASA Glenn Research Center's COMETBOARDS design optimization testbed were extended to generate approximate models for the PAX-300 aircraft engine. The analytical model of the engine is defined through nine variables: the fan efficiency factor, the low pressure of the compressor, the high pressure of the compressor, the high pressure of the turbine, the low pressure of the turbine, the operating pressure, and three critical temperatures (T(sub 4), T(sub vane), and T(sub metal)). Numerical Propulsion System Simulation (NPSS) calculations of the specific fuel consumption (TSFC), as a function of the variables can become time consuming, and numerical instabilities can occur during these design calculations. "Soft" models can alleviate both deficiencies. These approximate models are generated from a set of high-fidelity input-output pairs obtained from the NPSS code and a design of the experiment strategy. A neural network and a regression model with 45 weight factors were trained for the input/output pairs. Then, the trained models were validated through a comparison with the original NPSS code. Comparisons of TSFC versus the operating pressure and of TSFC versus the three temperatures (T(sub 4), T(sub vane), and T(sub metal)) are depicted in the figures. The overall performance was satisfactory for both the regression and the neural network model. The regression model required fewer calculations than the neural network model, and it produced marginally superior results. Training the approximate methods is time consuming. Once trained, the approximate methods generated the solution with only a trivial computational effort, reducing the solution time from hours to less than a minute

Optimality of a Fully Stressed Design

For a truss a fully stressed state is reached and when all its members are utilized to their full strength capacity. Historically, engineers considered such a design optimum. But recently this optimality has been questioned, especially since the weight of the structure is not explicitly used in fully stressed design calculations. This paper examines optimality of the full stressed design (FSD) with analytical and graphical illustrations. Solutions for a set of examples obtained by using the FSD method and optimization methods numerically confirm the optimality of the FSD. The FSD, which can be obtained with a small amount of calculation, can be extended to displacement constraints and to nontruss-type structures

Improved accuracy for finite element structural analysis via a new integrated force method

A comparative study was carried out to determine the accuracy of finite element analyses based on the stiffness method, a mixed method, and the new integrated force and dual integrated force methods. The numerical results were obtained with the following software: MSC/NASTRAN and ASKA for the stiffness method; an MHOST implementation method for the mixed method; and GIFT for the integrated force methods. The results indicate that on an overall basis, the stiffness and mixed methods present some limitations. The stiffness method generally requires a large number of elements in the model to achieve acceptable accuracy. The MHOST method tends to achieve a higher degree of accuracy for course models than does the stiffness method implemented by MSC/NASTRAN and ASKA. The two integrated force methods, which bestow simultaneous emphasis on stress equilibrium and strain compatibility, yield accurate solutions with fewer elements in a model. The full potential of these new integrated force methods remains largely unexploited, and they hold the promise of spawning new finite element structural analysis tools

Primal and Dual Integrated Force Methods Used for Stochastic Analysis

At the NASA Glenn Research Center, the primal and dual integrated force methods are being extended for the stochastic analysis of structures. The stochastic simulation can be used to quantify the consequence of scatter in stress and displacement response because of a specified variation in input parameters such as load (mechanical, thermal, and support settling loads), material properties (strength, modulus, density, etc.), and sizing design variables (depth, thickness, etc.). All the parameters are modeled as random variables with given probability distributions, means, and covariances. The stochastic response is formulated through a quadratic perturbation theory, and it is verified through a Monte Carlo simulation

Optimization of aerospace structures

Research carried out is grouped under two topics: (1) Design Optimization, and (2) Integrated Force Method of Analysis. Design Optimization Research Topics are singularity alleviation enhances structural optimization methods, computer based design capability extended through substructure synthesis, and optimality criteria provides optimum design for a select class of structural problems. Integrated Force Method of Analysis Research Topics are boundary compatibility formulation improves stress analysis of shell structures. Brief descriptions of the four topics are appended

Reliability-Based Design Optimization of a Composite Airframe Component

A stochastic optimization methodology (SDO) has been developed to design airframe structural components made of metallic and composite materials. The design method accommodates uncertainties in load, strength, and material properties that are defined by distribution functions with mean values and standard deviations. A response parameter, like a failure mode, has become a function of reliability. The primitive variables like thermomechanical loads, material properties, and failure theories, as well as variables like depth of beam or thickness of a membrane, are considered random parameters with specified distribution functions defined by mean values and standard deviations