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...

Topics: NASA Technical Reports Server (NTRS), MULTIDISCIPLINARY DESIGN OPTIMIZATION, STOCHASTIC PROCESSES,...

The theory and user instructions for an optimization code based on the method of feasible directions are presented. The code was written for wide distribution and ease of attachment to other simulation software. Although the theory of the method of feasible direction was developed in the 1960's, many considerations are involved in its actual implementation as a computer code. Included in the code are a number of features to improve robustness in optimization. The search direction is obtained by...

Topics: NASA Technical Reports Server (NTRS), ALGORITHMS, COMPUTER PROGRAMS, COMPUTERIZED SIMULATION,...

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...

Topics: NASA Technical Reports Server (NTRS), TRUSSES, DESIGN, LOAD DISTRIBUTION (FORCES), LOADS (FORCES),...

Design optimization of large systems can be attempted through a sub-problem strategy. In this strategy, the original problem is divided into a number of smaller problems that are clustered together to obtain a sequence of sub-problems. Solution to the large problem is attempted iteratively through repeated solutions to the modest sub-problems. This strategy is applicable to structures and to multidisciplinary systems. For structures, clustering the substructures generates the sequence of...

Topics: NASA Technical Reports Server (NTRS), NEURAL NETS, DESIGN OPTIMIZATION, SUBSTRUCTURES, SENSITIVITY...

Design sensitivity is central to most optimization methods. The analytical sensitivity expression for an indeterminate structural design optimization problem can be factored into a simple determinate term and a complicated indeterminate component. Sensitivity can be approximated by retaining only the determinate term and setting the indeterminate factor to zero. The optimum solution is reached with the approximate sensitivity. The central processing unit (CPU) time to solution is substantially...

Topics: NASA Technical Reports Server (NTRS), DESIGN OPTIMIZATION, SENSITIVITY, STRUCTURAL DESIGN,...

Structural design generated by traditional method, optimization method and the stochastic design concept are compared. In the traditional method, the constraints are manipulated to obtain the design and weight is back calculated. In design optimization, the weight of a structure becomes the merit function with constraints imposed on failure modes and an optimization algorithm is used to generate the solution. Stochastic design concept accounts for uncertainties in loads, material properties,...

Topics: NASA Technical Reports Server (NTRS), DESIGN OPTIMIZATION, NONLINEAR PROGRAMMING, STOCHASTIC...

A reliability-based optimization methodology has been developed to design the raked wing tip of the Boeing 767-400 extended range airliner made of composite and metallic materials. Design is formulated for an accepted level of risk or reliability. The design variables, weight and the constraints became functions of reliability. Uncertainties in the load, strength and the material properties, as well as the design variables, were modeled as random parameters with specified distributions, like...

Topics: NASA Technical Reports Server (NTRS), COMPOSITE MATERIALS, AIRFRAMES, WINGS, DESIGN ANALYSIS, LOADS...

Dynamic animation of stresses and displacements, which complement each other, can be a useful tool in the analysis and design of structural components. At the present time only displacement-mode animation is available through the popular stiffness formulation. This paper attempts to complete this valuable visualization tool by augmenting the existing art with stress mode animation. The reformulated method of forces, which in the literature is known as the integrated force method (IFM), became...

Topics: NASA Technical Reports Server (NTRS), STRESS ANALYSIS, STRUCTURAL DESIGN, DESIGN ANALYSIS,...

The merits and limitations of the optimality criteria (OC) method for the minimum weight design of structures subjected to multiple load conditions under stress, displacement, and frequency constraints were investigated by examining several numerical examples. The examples were solved utilizing the Optimality Criteria Design Code that was developed for this purpose at NASA Lewis Research Center. This OC code incorporates OC methods available in the literature with generalizations for stress...

Topics: NASA Technical Reports Server (NTRS), COMPUTER AIDED DESIGN, OPTIMIZATION, STRUCTURAL DESIGN,...

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...

Topics: NASA Technical Reports Server (NTRS), STOCHASTIC PROCESSES, PROBABILITY DISTRIBUTION FUNCTIONS,...

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...

Topics: NASA Technical Reports Server (NTRS), MICHELL THEOREM, POLAR COORDINATES, PARAMETERIZATION,...

The theory of elasticity evolved over centuries through the contributions of eminent scientists like Cauchy, Navier, Hooke Saint Venant, and others. It was deemed complete when Saint Venant provided the strain formulation in 1860. However, unlike Cauchy, who addressed equilibrium in the field and on the boundary, the strain formulation was confined only to the field. Saint Venant overlooked the compatibility on the boundary. Because of this deficiency, a direct stress formulation could not be...

Topics: NASA Technical Reports Server (NTRS), MICHELL THEOREM, MATHEMATICAL MODELS, BOUNDARY CONDITIONS,...

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...

Topics: NASA Technical Reports Server (NTRS), COMPATIBILITY, EQUILIBRIUM EQUATIONS, FINITE ELEMENT METHOD,...

Strength of materials problems have been classified into determinate and indeterminate problems. Determinate analysis primarily based on the equilibrium concept is well understood. Solutions of indeterminate problems required additional compatibility conditions, and its comprehension was not exclusive. A solution to indeterminate problem is generated by manipulating the equilibrium concept, either by rewriting in the displacement variables or through the cutting and closing gap technique of the...

Topics: NASA Technical Reports Server (NTRS), STRUCTURAL ANALYSIS, COMPATIBILITY, DISPLACEMENT, EQUILIBRIUM...

At the NASA Glenn Research Center, the NASA engine performance program (NEPP, ref. 1) and the design optimization testbed COMETBOARDS (ref. 2) with regression and neural network analysis-approximators have been coupled to obtain a preliminary engine design methodology. The solution to a high-bypass-ratio subsonic waverotor-topped turbofan engine, which is shown in the preceding figure, was obtained by the simulation depicted in the following figure. This engine is made of 16 components mounted...

Topics: NASA Technical Reports Server (NTRS), ENGINE DESIGN, REGRESSION ANALYSIS, NEURAL NETS, DESIGN...

Two methods of solving indeterminate structural-mechanics problems have been developed as products of research on the theory of strain compatibility. In these methods, stresses are considered to be the primary unknowns (in contrast to strains and displacements being considered as the primary unknowns in some prior methods). One of these methods, denoted the integrated force method (IFM), makes it possible to compute stresses, strains, and displacements with high fidelity by use of modest...

Topics: NASA Technical Reports Server (NTRS), STRUCTURAL ANALYSIS, COMPUTATION, ELASTIC PROPERTIES,...

The design optimization of air-breathing propulsion engine concepts has been accomplished by soft-coupling the NASA Engine Performance Program (NEPP) analyzer with the NASA Lewis multidisciplinary optimization tool COMETBOARDS. Engine problems, with their associated design variables and constraints, were cast as nonlinear optimization problems with thrust as the merit function. Because of the large number of mission points in the flight envelope, the diversity of constraint types, and the...

Topics: NASA Technical Reports Server (NTRS), AIR BREATHING ENGINES, OPTIMIZATION, ENGINE DESIGN, 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...

Topics: NASA Technical Reports Server (NTRS), NEURAL NETS, DESIGN OPTIMIZATION, EXPERIMENT DESIGN,...

Design optimization of large structural systems can be attempted through a substructure strategy when convergence difficulties are encountered. When this strategy is used, the large structure is divided into several smaller substructures and a subproblem is defined for each substructure. The solution of the large optimization problem can be obtained iteratively through repeated solutions of the modest subproblems. Substructure strategies, in sequential as well as in parallel computational modes...

Topics: NASA Technical Reports Server (NTRS), MULTIPROCESSING (COMPUTERS), STRUCTURAL ANALYSIS,...

A wave rotor, which acts as a high-technology topping spool in gas turbine engines, can increase the effective pressure ratio as well as the turbine inlet temperature in such engines. The wave rotor topping, in other words, may significantly enhance engine performance by increasing shaft horse power while reducing specific fuel consumption. This performance enhancement requires optimum selection of the wave rotor's adjustable parameters for speed, surge margin, and temperature constraints...

Topics: NASA Technical Reports Server (NTRS), GAS TURBINE ENGINES, WAVE ROTORS, SPOOLS, ENGINE ANALYZERS,...

At the NASA Glenn Research Center, NASA Langley Research Center's Flight Optimization System (FLOPS) and the design optimization testbed COMETBOARDS with regression and neural-network-analysis approximators have been coupled to obtain a preliminary aircraft design methodology. For a subsonic aircraft, the optimal design, that is the airframe-engine combination, is obtained by the simulation. The aircraft is powered by two high-bypass-ratio engines with a nominal thrust of about 35,000 lbf. It...

Topics: NASA Technical Reports Server (NTRS), APPROXIMATION, NEURAL NETS, SUBSONIC AIRCRAFT, REGRESSION...

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...

Topics: NASA Technical Reports Server (NTRS), COMPUTER PROGRAMS, QUADRATIC PROGRAMMING, CRAY COMPUTERS,...

The theory of elasticity has camouflaged a deficiency in the compatibility formulation since 1860. In structures the ad hoc compatibility conditions through virtual "cuts" and closing "gaps" are not parallel to the strain formulation in elasticity. This deficiency in the compatibility conditions has prevented the development of a direct stress determination method in structures and in elasticity. We have addressed this deficiency and attempted to unify the theory of...

Topics: NASA Technical Reports Server (NTRS), COMPATIBILITY, ELASTIC PROPERTIES, FINITE ELEMENT METHOD,...

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...

Topics: NASA Technical Reports Server (NTRS), COMPOSITE MATERIALS, DESIGN OPTIMIZATION, RELIABILITY,...

In elasticity, the method of forces, wherein stress parameters are considered as the primary unknowns, is known as the Beltrami-Michell formulation (BMF). The existing BMF can only solve stress boundary value problems; it cannot handle the more prevalent displacement of mixed boundary value problems of elasticity. Therefore, this formulation, which has restricted application, could not become a true alternative to the Navier's displacement method, which can solve all three types of boundary...

Topics: NASA Technical Reports Server (NTRS), BOUNDARY VALUE PROBLEMS, CIRCULAR PLATES, CYLINDRICAL SHELLS,...

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...

Topics: NASA Technical Reports Server (NTRS), DISPLACEMENT, EQUILIBRIUM EQUATIONS, FINITE ELEMENT METHOD,...

Nonlinear programming algorithms play an important role in structural design optimization. Fortunately, several algorithms with computer codes are available. At NASA Lewis Research Center, a project was initiated to assess performance of 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 different optimizers on a...

Topics: NASA Technical Reports Server (NTRS), ALGORITHMS, NONLINEAR PROGRAMMING, STRUCTURAL DESIGN,...

A force method formulation, the completed Beltrami-Michell formulation (CBMF), has been developed for analyzing boundary value problems in elastic continua. The CBMF is obtained by augmenting the classical Beltrami-Michell formulation with novel boundary compatibility conditions. It can analyze general elastic continua with stress, displacement, or mixed boundary conditions. The CBMF alleviates the limitations of the classical formulation, which can solve stress boundary value problems only. In...

Topics: NASA Technical Reports Server (NTRS), BOUNDARY VALUE PROBLEMS, ELASTIC BODIES, PLATES (STRUCTURAL...

The NASA Engine Performance Program (NEPP) can configure and analyze almost any type of gas turbine engine that can be generated through the interconnection of a set of standard physical components. In addition, the code can optimize engine performance by changing adjustable variables under a set of constraints. However, for engine cycle problems at certain operating points, the NEPP code can encounter difficulties: nonconvergence in the currently implemented Powell's optimization algorithm and...

Topics: NASA Technical Reports Server (NTRS), AIRCRAFT ENGINES, NEURAL NETS, REGRESSION ANALYSIS,...

The application of artificial neural networks to capture structural design expertise is demonstrated. The principal advantage of a trained neural network is that it requires trivial computational effort to produce an acceptable new design. For the class of problems addressed, the development of a conventional expert system would be extremely difficult. In the present effort, a structural optimization code with multiple nonlinear programming algorithms and an artificial neural network code NETS...

Topics: NASA Technical Reports Server (NTRS), AEROSPACE SYSTEMS, AIRCRAFT DESIGN, COMPUTER AIDED DESIGN,...

The basic theory of solid mechanics was deemed complete circa 1860 when St. Venant provided the strain formulation or the field compatibility condition. The strain formulation was incomplete. The missing portion has been formulated and identified as the boundary compatibility condition (BCC). The BCC, derived through a variational formulation, has been verified through integral theorem and solution of problems. The BCC, unlike the field counterpart, do not trivialize when expressed in...

Topics: NASA Technical Reports Server (NTRS), MATHEMATICAL MODELS, SOLID MECHANICS, MECHANICAL PROPERTIES,...

Design optimization for subsonic and supersonic aircraft and for air-breathing propulsion engine concepts has been accomplished by soft-coupling the Flight Optimization System (FLOPS) and the NASA Engine Performance Program analyzer (NEPP), to the NASA Lewis multidisciplinary optimization tool COMETBOARDS. Aircraft and engine design problems, with their associated constraints and design variables, were cast as nonlinear optimization problems with aircraft weight and engine thrust as the...

Topics: NASA Technical Reports Server (NTRS), AIR BREATHING ENGINES, AIRCRAFT DESIGN, AIRCRAFT ENGINES,...

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...

Topics: NASA Technical Reports Server (NTRS), DESIGN ANALYSIS, LOADING MOMENTS, NEURAL NETS, OPTIMIZATION,...

Minimizing the weight of structural components of the space station launched into orbit in a space shuttle can save cost, reduce the number of space shuttle missions, and facilitate on-orbit fabrication. Traditional manual design of such components, although feasible, cannot represent a minimum weight condition. At NASA Lewis Research Center, a design capability called CometBoards (Comparative Evaluation Test Bed of Optimization and Analysis Routines for the Design of Structures) has been...

Topics: NASA Technical Reports Server (NTRS), COMPUTER AIDED DESIGN, SPACE STATION FREEDOM, SPACE STATION...

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...

Topics: NASA Technical Reports Server (NTRS), COMPUTER PROGRAMS, FINITE ELEMENT METHOD, MATHEMATICAL...

The Integrated Force Method has been developed in recent years for the analysis of structural mechanics problems. This method treats all independent internal forces as unknown variables that can be calculated by simultaneously imposing equations of equilibrium and compatibility conditions. In this paper a finite element library for analyzing two-dimensional problems by the Integrated Force Method is presented. Triangular- and quadrilateral-shaped elements capable of modeling arbitrary domain...

Topics: NASA Technical Reports Server (NTRS), FINITE ELEMENT METHOD, STRUCTURAL ANALYSIS, STRESS...

The Flight-Optimization-System (FLOPS) code encountered difficulty in analyzing a subsonic aircraft. The limitation made the design optimization problematic. The deficiencies have been alleviated through use of neural network and regression approximations. The insight gained from using the approximators is discussed in this paper. The FLOPS code is reviewed. Analysis models are developed and validated for each approximator. The regression method appears to hug the data points, while the neural...

Topics: NASA Technical Reports Server (NTRS), AIRCRAFT DESIGN, DESIGN OPTIMIZATION, NEURAL NETS,...

The Integrated Force Method, a recently developed method for analyzing structures, is extended in this paper to three-dimensional structural analysis. First, a general formulation is developed to generate the stress interpolation matrix in terms of complete polynomials of the required order. The formulation is based on definitions of the stress tensor components in term of stress functions. The stress functions are written as complete polynomials and substituted into expressions for stress...

Topics: NASA Technical Reports Server (NTRS), FINITE ELEMENT METHOD, STRESS ANALYSIS, STRESS DISTRIBUTION,...

The strain formulation in elasticity and the compatibility condition in structural mechanics have neither been understood nor have they been utilized. This shortcoming prevented the formulation of a direct method to calculate stress. We have researched and understood the compatibility condition for linear problems in elasticity and in finite element analysis. This has lead to the completion of the method of force with stress (or stress resultant) as the primary unknown. The method in elasticity...

Topics: NASA Technical Reports Server (NTRS), COMPATIBILITY, DESIGN OPTIMIZATION, ELASTIC PROPERTIES,...

A general purpose optimization tool for multidisciplinary applications, which in the literature is known as COMETBOARDS, is being developed at NASA Lewis Research Center. The modular organization of COMETBOARDS includes several analyzers and state-of-the-art optimization algorithms along with their cascading strategy. The code structure allows quick integration of new analyzers and optimizers. The COMETBOARDS code reads input information from a number of data files, formulates a design as a set...

Topics: NASA Technical Reports Server (NTRS), NONLINEAR PROGRAMMING, MULTIDISCIPLINARY DESIGN OPTIMIZATION,...

A research project to comparatively evaluate 10 nonlinear optimization algorithms was recently completed. A conclusion was that no single optimizer could successfully solve all 40 problems in the test bed, even though most optimizers successfully solved at least one-third of the problems. We realized that improved search directions and step lengths, available in the 10 optimizers compared, were not likely to alleviate the convergence difficulties. For the solution of those difficult problems we...

Topics: NASA Technical Reports Server (NTRS), MULTIDISCIPLINARY DESIGN OPTIMIZATION, ALGORITHMS, AIRCRAFT...

Several nonlinear mathematical programming algorithms for structural design applications are available at present. These include the sequence of unconstrained minimizations technique, the method of feasible directions, and the sequential quadratic programming technique. The optimality criteria technique and the fully utilized design concept are two other structural design methods. A project was undertaken to bring all these design methods under a common computer environment so that a designer...

Topics: NASA Technical Reports Server (NTRS), ALGORITHMS, COMPUTER PROGRAMS, DESIGN ANALYSIS, FINITE...