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Computer programs for synthesizing structural arrangements for ring-stiffened, honeycomb sandwich, and ring-stringer stiffened methods of construction for Saturn nose fairings
Ongoing research and testing are essential in the development of air-breathing hypersonic propulsion technology, and this year some positive advancement was made at the NASA Glenn Research Center. Recent work performed for GTX, a rocket-based combined-cycle, single-stage-to-orbit concept, included structural assessments of both the engine and flight vehicle. In the development of air-breathing engine technology, it is impractical to design and optimize components apart from the fully integrated system because tradeoffs must be made between performance and structural capability. Efforts were made to control the flight trajectory, for example, to minimize the aerodynamic heating effects. Structural optimization was applied to evaluate concept feasibility and was instrumental in the determination of the gross liftoff weight of the integrated system. Achieving low Earth orbit with even a small payload requires an aggressive approach to weight minimization through the use of lightweight, oxidation-resistant composite materials. Assessing the integrated system involved investigating the flight trajectory to determine where the critical load events occur in flight and then generating the corresponding environment at each of these events. Structural evaluation requires the mapping of the critical flight loads to finite element models, including the combined effects of aerodynamic, inertial, combustion, and other loads. NASA s APAS code was used to generate aerodynamic pressure and temperature profiles at each critical event. The radiation equilibrium surface temperatures from APAS were used to predict temperatures through the thickness. Heat transfer solutions using NASA's MINIVER code and the SINDA code (Cullimore & Ring Technologies, Littleton, CO) were calculated at selective points external to the integrated vehicle system and then extrapolated over the entire exposed surface. FORTRAN codes were written to expedite the finite element mapping of the aerodynamic heating effects for the internal structure.
A quadratic extended interior penalty function formulation especially well suited for second-order unconstrained optimization procedures is presented. Analytical derivatives of constraints and an approximate analysis technique are used. Minimum-mass design results are presented which indicate that the combination of these procedures can help make mathematical programming a useful optimization tool for large-order structural design problems with a large number of design variables and multiple constraints. Examples include statically loaded high- and low-aspect-ratio wings simultaneously subjected to stress, displacement, minimum gage and, in some cases, maximum strain constraints.
The application of formal optimization techniques to the design of large engineering structures such as aircraft is presently hindered in connection with the large number of design variables involved. According to an approach which attempts to overcome the difficulties, the problem is broken up into several smaller subproblems. This approach has, however, weaknesses which may prevent a determination of the minimum structural weight. Schmit and Ramanathan (1973) have developed a method, which is designed to incorporate control of the material distribution among the finite elements of an assembled structure for a two-level optimization. However, the optimization schemes considered would not be suitable to optimization schemes considered would not be suitable to multidisciplinary optimization of large engineering systems. Sobieszczanski-Sobieski (1982) proposed a method for decomposing a large multidisciplinary optimization problem into a number of small subproblems. The present investigation is concerned with the implementation of this method.
The feasibility of adding viscoelasticity and the Generalized Method of Cells (GMC) for micromechanical viscoelastic behavior into the commercial HyperSizer structural analysis and optimization code was investigated. The viscoelasticity methodology was developed in four steps. First, a simplified algorithm was devised to test the iterative time stepping method for simple one-dimensional multiple ply structures. Second, GMC code was made into a callable subroutine and incorporated into the one-dimensional code to test the accuracy and usability of the code. Third, the viscoelastic time-stepping and iterative scheme was incorporated into HyperSizer for homogeneous, isotropic viscoelastic materials. Finally, the GMC was included in a version of HyperSizer. MS Windows executable files implementing each of these steps is delivered with this report, as well as source code. The findings of this research are that both viscoelasticity and GMC are feasible and valuable additions to HyperSizer and that the door is open for more advanced nonlinear capability, such as viscoplasticity.
A next generation reusable launch vehicle (RLV) will require thermally efficient and light-weight cryogenic propellant tank structures. Since these tanks will be weight-critical, analytical tools must be developed to aid in sizing the thickness of insulation layers and structural geometry for optimal performance. Finite element method (FEM) models of the tank and insulation layers were created to analyze the thermal performance of the cryogenic insulation layer and thermal protection system (TPS) of the tanks. The thermal conditions of ground-hold and re-entry/soak-through for a typical RLV mission were used in the thermal sizing study. A general-purpose nonlinear FEM analysis code, capable of using temperature and pressure dependent material properties, was used as the thermal analysis code. Mechanical loads from ground handling and proof-pressure testing were used to size the structural geometry of an aluminum cryogenic tank wall. Nonlinear deterministic optimization and reliability optimization techniques were the analytical tools used to size the geometry of the isogrid stiffeners and thickness of the skin. The results from the sizing study indicate that a commercial FEM code can be used for thermal analyses to size the insulation thicknesses where the temperature and pressure were varied. The results from the structural sizing study show that using combined deterministic and reliability optimization techniques can obtain alternate and lighter designs than the designs obtained from deterministic optimization methods alone.
Passenger comfort is of great importance in most transport vehicles. For instance, in the new generation of regional turboprop aircraft, a low noise level is vital to be competitive on the market. The possibilities to predict noise levels analytically has improved rapidly in recent years. This will make it possible to take acoustic design criteria into account in early project stages. The development of the ASKA FE-system to include also acoustic analysis has been carried out at Saab Aircraft Division and the Aeronautical Research Institute of Sweden in a joint project. New finite elements have been developed to model the free fluid, porous damping materials, and the interaction between the fluid and structural degrees of freedom. The FE approach to the acoustic analysis is best suited for lower frequencies up to a few hundred Hz. For accurate analysis of interior cabin noise, large 3-D FE-models are built, but 2-D models are also considered to be useful for parametric studies and optimization. The interest is here focused on the introduction of an acoustic design criteria in the general structural optimization system OPTSYS available at the Saab Aircraft Division. The first implementation addresses a somewhat limited class of problems. The problems solved are formulated: Minimize the structural weight by modifying the dimensions of the structure while keeping the noise level in the cavity and other structural design criteria within specified limits.
The purpose of the research is to study the integration of structural, dynamic, and aerodynamic considerations in the design-optimization process for helicopter rotorblades. This is to be done in three phases. Task 1 is to bring on-line computer codes that could perform the finite-element frequency analyses of rotor blades. The major features of this program are summarized. The second task was to bring on-line an optimization code for the work. Several were tried and it was decided to use CONMIN. Explicit volume constraints on the thicknesses and lumped masses used in the optimization were added. The specific aeroelastic constraint that the center of mass must be forward of the quarter chord in order to prevent flutter was applied. The bending-torsion coupling due to cg-ea offset within the blade cross section was included. Also included were some very simple stress constraints. The first three constraints are completed, and the fourth constraint is being completed.
The differences between fully stressed and minimum-weight joined-wing structures are identified, and these differences are quantified in terms of weight, stress, and direct operating cost. A numerical optimization method and a fully stressed design method are used to design joined-wing structures. Both methods determine the sizes of 204 structural members, satisfying 1020 stress constraints and five buckling constraints. Monotonic splines are shown to be a very effective way of linking spanwise distributions of material to a few design variables. Both linear and nonlinear analyses are employed to formulate the buckling constraints. With a constraint on buckling, the fully stressed design is shown to be very similar to the minimum-weight structure. It is suggested that a fully stressed design method based on nonlinear analysis is adequate for an aircraft optimization study.
The paper presents a finite element method for minimum weight design of structures with lower-bound constraints on the natural frequencies, and upper and lower bounds on the design variables. The design algorithm is essentially an iterative solution of the Kuhn-Tucker optimality criterion. The three most important features of the algorithm are: (1) a small number of design iterations are needed to reach optimal or near-optimal design, (2) structural elements with a wide variety of size-stiffness may be used, the only significant restriction being the exclusion of curved beam and shell elements, and (3) the algorithm will work for multiple as well as single frequency constraints. The design procedure is illustrated with three simple problems.
This paper describes an optimization procedure for the minimum weight design of complex structures. The procedure is based on a new cubic extended interior penalty function (CEIPF) used with the sequence of unconstrained minimization technique (SUMT) and Newton's method. The Hessian matrix of the penalty function is approximated using only constraints and their derivatives. The CEIPF is designed to minimize the error in the approximation of the Hessian matrix, and as a result the number of structural analyses required is small and independent of the number of design variables. Three example problems are reported. The number of structural analyses is reduced by as much as 50 per cent below previously reported results.
The minimum weight optimum design of damped linearly elastic structural systems subjected to periodic loading with behavior constraints on maximum deflections and side constraints on design variables is addressed. Attention is focused on the two major impediments to an optimal solution: (1) the time parametric nature of the behavior constraints; and (2) the severe nonconvexity of the design space. A solution method based on upper bound approximations for the behavior constraints and an innovative mathematical programming scheme for seeking the optimal frequency subspace is set forth. Numerical results for several test problems illustrate the effectiveness of the method reported.
Various attempts have been made to construct a rigorous mathematical theory of optimization for size, shape, and topology (i.e. layout) of an elastic structure. If these are represented by a finite number of parametric functions, as Armand described, it is possible to construct an existence theory of the optimum design using compactness argument in a finite dimensional design space or a closed admissible set of a finite dimensional design space. However, if the admissible design set is a subset of non-reflexive Banach space such as L(sup infinity)(Omega), construction of the existence theory of the optimum design becomes suddenly difficult and requires to extend (i.e. generalize) the design problem to much more wider class of design that is compatible to mechanics of structures in the sense of variational principle. Starting from the study by Cheng and Olhoff, Lurie, Cherkaev, and Fedorov introduced a new concept of convergence of design variables in a generalized sense and construct the 'G-Closure' theory of an extended (relaxed) optimum design problem. A similar attempt, but independent in large extent, can also be found in Kohn and Strang in which the shape and topology optimization problem is relaxed to allow to use of perforated composites rather than restricting it to usual solid structures. An identical idea is also stated in Murat and Tartar using the notion of the homogenization theory. That is, introducing possibility of micro-scale perforation together with the theory of homogenization, the optimum design problem is relaxed to construct its mathematical theory. It is also noted that this type of relaxed design problem is perfectly matched to the variational principle in structural mechanics.
Summarized here is the first six years of research into the integration of structural, dynamic, and aerodynamic considerations in the design-optimization process for rotor blades. Specifically discussed here is the application of design optimization techniques for helicopter rotor blades. The reduction of vibratory shears and moments at the blade root, aeroelastic stability of the rotor, optimum airframe design, and an efficient procedure for calculating system sensitivities with respect to the design variables used are discussed.
A procedure is presented for the minimization of structural mass while satisfying flutter speed constraints. The procedure differs from other optimization methods in that the flutter speed is exactly satisfied at each resizing step, and the step size is determined by a direct minimization of the objective function (mass) for each set of flutter derivatives calculated. In conjunction with this method, a new move vector is suggested which results in a very efficient resizing procedure.
A comparison is made of results obtained from mathematical programming and optimality criteria procedures for the minimum-mass design of typical aircraft wing structures to satisfy prescribed flutter requirements. The mathematical programming method is based on an interior penalty function approach. A rigorous optimality criterion and an intuitive optimality criterion based on uniform strain energy density are considered. An intuitive resizing procedure is used for both optimality criterion solutions. All results are calculated using the same computer program, changing only the optimization procedure. Both high- and low-aspect-ratio wings are examined. Finite elements are used for structural modeling, and the generalized coordinates for the flutter solution are based on the natural vibration modes of the structure.
This paper presents the application of the NMBM to obtain a minimum weight structure with constraints on displacements and minimum sizes. The solution to the problem is obtained via minimizing the Modified Barrier Function (MBF) at each step by using the Newton Method and updating Lagrange multipliers. The Lagrange multipliers are updated by using the value of the constraints at the minimum of the MBF. Three truss problems with a different number of design variables are solved. The convergence to the minimum weight design was found to be monotonic and the algorithm is potentially robust for solving problems with a large number of design variables.
Mathematical programming techniques provide a general approach to automated structural design. An iterative method is proposed in which design is treated as a hierarchy of subproblems, one being locally constrained and the other being locally unconstrained. It is assumed that the design space is locally convex in the case of good initial designs and that the objective and constraint functions are continuous, with continuous first derivatives. A general design algorithm is outlined for finding a move direction which will decrease the value of the objective function while maintaining a feasible design. The case of one-dimensional search in a two-variable design space is discussed. Possible applications are discussed. A major feature of the proposed algorithm is its application to problems which are inherently ill-conditioned, such as design of structures for optimum geometry.