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At least 37 records · Page 2

Multi-objective shape and material optimization of composite structures including damping

A multi-objective optimal design methodology is developed for light-weight, low-cost composite structures of improved dynamic performance. The design objectives include minimization of resonance amplitudes (or maximization of modal damping), weight, and material cost. The design vector includes micromechanics, laminate, and structural shape parameters. Performance constraints are imposed on static displacements, dynamic amplitudes, and natural frequencies. The effects of damping on the dynamics of composite structures are incorporated. Preliminary applications on a cantilever composite beam illustrated that only the proposed multi-objective optimization, as opposed to single objective functions, simultaneously improved all objectives. The significance of composite damping in the design of advanced composite structures was also demonstrated, indicating that design methods based on undamped dynamics may fail to improve the dynamic performance near resonances.

Saravanos, D. A.↗

Composite laminate optimization program suitable for microcomputers

The design of a composite panel requires some way of finding the minimum thickness laminate which will withstand the load requirements without failure. The mathematical complexity of this problem dictates the use of nonlinear optimization techniques. Specialized laminate optimization programs were developed which are compact and efficient enough to run on microcomputers. Only stresses at a point and inplane loads and deflections are considered. The programs are simple to use and require no knowledge of optimization. Techniques are developed which find minimum thickness laminates with either ply ratios or ply angles as design variables. A method is presented for finding the optimum orientation for the axis of symmetry of an orthotropic laminate. The orthotropic laminate program uses an approximate failure theory, which speed up computations dramatically.

Flanagan, G. V.↗

Local design optimization for composite transport fuselage crown panels

Composite transport fuselage crown panel design and manufacturing plans were optimized to have projected cost and weight savings of 18 and 45 percent, respectively. These savings are close to those quoted as overall NASA Advanced Composite Technology (ACT) program goals. Three local optimization tasks were found to influence the cost and weight of fuselage crown panels. The effects are summarized of each task and the task associated with a design cost model is described in detail. Studies were performed to evaluate the relationship between manufacturing cost and design details. A design tool was developed to aid in these studies. The development of the design tool included combining cost and performance constraints with a random search optimization algorithm. The resulting software was used in a series of optimization studies that evaluated the sensitivity of design variables, guidelines, criteria, and material selection on cost. The effect of blending adjacent design points in a full scale panel subjected to changing load distributions and local variations was shown to be important. Technical issues and directions for future work were identified.

Swanson, G. D.↗

Local design optimization for composite transport fuselage crown panels

Composite transport fuselage crown panel design and manufacturing plans were optimized to have projected cost and weight savings of 18 percent and 45 percent, respectively. These savings are close to those quoted as overall NASA ACT program goals. Three local optimization tasks were found to influence the cost and weight of fuselage crown panels. This paper summarizes the effect of each task and describes in detail the task associated with a design cost model. Studies were performed to evaluate the relationship between manufacturing cost and design details. A design tool was developed to aid in these investigations. The development of the design tool included combining cost and performance constraints with a random search optimization algorithm. The resulting software was used in a series of optimization studies that evaluated the sensitivity of design variables, guidelines, criteria, and material selection on cost. The effect of blending adjacent design points in a full scale panel subjected to changing load distributions and local variations was shown to be important. Technical issues and directions for future work were identified.

Swanson, G. D.↗

Multi-parameter optimization tool for low-cost commercial fuselage crown designs

The work in progress for developing a methodology and software tool to aid in the optimal design of composite structures is discussed. The methodology is being developed to take advantage of the ability to tailor the composite material in conjunction with the design of the structure. The composites optimization design software UWCODA was found to be very successful in preliminary testing and early experience. UWCODA is a composites design code that uses a number of plies and fiber angles as design variables, employs maximum strain failure criteria for objective function and additional constraints, includes Boeing design tools for stiffened panels, and includes stiffener geometry in the design variables.

Zabinsky, Zelda↗

Sensitivity and optimization of composite structures using MSC/NASTRAN

Design sensitivity analysis for composites will soon be available in MSC/NASTRAN. The design variables for composites can be lamina thicknesses, orientation angles, material properties or a combination of all three. With the increasing use of composites in aerospace and automotive industries, this general capability can be used in its own right for carrying out sensitivity analysis of complicated real-life structures. As part of a research effort, the sensitivity analysis was coupled with a general purpose optimizer. This preliminary version of the optimizer is capable of dealing with minimum weight structural design with a rather general design variable linking capability at the element level or system level. Only sizing type of design variables (i.e., lamina thicknesses) can be handled by the optimizer. Test cases were run and validated by comparison with independent finite element packages. The linking of design sensitivity capability for composites in MSC/NASTRAN with an optimizer would give designers a powerful automated tool to carry out practical opitmization design of real-life complicated composite structures.

Nagendra, Gopal K.↗

Finite element analysis and optimization of composite structures

Linearly elastic fiber reinforced composite discs and laminates in plane stress with variable local orientation and concentration of one or two fiber fields embedded in the matrix material, are considered. The thicknesses and the domain of the discs or laminates are assumed to be given, together with prescribed boundary conditions and in-plane loading along the edge. The problem under study consists in determining throughout the structural domain the optimum orientations and concentrations of the fiber fields in such a way as to maximize the integral stiffness of the composite disc or laminate under the seven loading. Minimization of the integral stiffness can also be performed. The optimization is performed subject to a prescribed bound on the total cost or weight of the composite that for given unit cost factors or specific weights determines the amounts of fiber and matrix materials in the structure. Examples are presented.

Thomsen, Jan↗

Reliability Sensitivity Analysis and Design Optimization of Composite Structures Based on Response Surface Methodology

This report discusses the development and application of two alternative strategies in the form of global and sequential local response surface (RS) techniques for the solution of reliability-based optimization (RBO) problems. The problem of a thin-walled composite circular cylinder under axial buckling instability is used as a demonstrative example. In this case, the global technique uses a single second-order RS model to estimate the axial buckling load over the entire feasible design space (FDS) whereas the local technique uses multiple first-order RS models with each applied to a small subregion of FDS. Alternative methods for the calculation of unknown coefficients in each RS model are explored prior to the solution of the optimization problem. The example RBO problem is formulated as a function of 23 uncorrelated random variables that include material properties, thickness and orientation angle of each ply, cylinder diameter and length, as well as the applied load. The mean values of the 8 ply thicknesses are treated as independent design variables. While the coefficients of variation of all random variables are held fixed, the standard deviations of ply thicknesses can vary during the optimization process as a result of changes in the design variables. The structural reliability analysis is based on the first-order reliability method with reliability index treated as the design constraint. In addition to the probabilistic sensitivity analysis of reliability index, the results of the RBO problem are presented for different combinations of cylinder length and diameter and laminate ply patterns. The two strategies are found to produce similar results in terms of accuracy with the sequential local RS technique having a considerably better computational efficiency.

Rais-Rohani, Masoud↗

Aeroelasticity and structural optimization of composite helicopter rotor blades with swept tips

This report describes the development of an aeroelastic analysis capability for composite helicopter rotor blades with straight and swept tips, and its application to the simulation of helicopter vibration reduction through structural optimization. A new aeroelastic model is developed in this study which is suitable for composite rotor blades with swept tips in hover and in forward flight. The hingeless blade is modeled by beam type finite elements. A single finite element is used to model the swept tip. Arbitrary cross-sectional shape, generally anisotropic material behavior, transverse shears and out-of-plane warping are included in the blade model. The nonlinear equations of motion, derived using Hamilton's principle, are based on a moderate deflection theory. Composite blade cross-sectbnal properties are calculated by a separate linear, two-dimensional cross section analysis. The aerodynamic loads are obtained from quasi-steady, incompressible aerodynamics, based on an implicit formulation. The trim and steady state blade aeroelastic response are solved in a fully coupled manner. In forward flight, where the blade equations of motion are periodic, the coupled trim-aeroelastic response solution is obtained from the harmonic balance method. Subsequently, the periodic system is linearized about the steady state response, and its stability is determined from Floquet theory.

Yuan, K. A.↗

Variable Complexity Optimization of Composite Structures

The use of several levels of modeling in design has been dubbed variable complexity modeling. The work under the grant focused on developing variable complexity modeling strategies with emphasis on response surface techniques. Applications included design of stiffened composite plates for improved damage tolerance, the use of response surfaces for fitting weights obtained by structural optimization, and design against uncertainty using response surface techniques.

Haftka, Raphael T.↗

Variable Complexity Optimization of Composite Structures

The use of several levels of modeling in design has been dubbed variable complexity modeling. The work under the grant focused on developing variable complexity modeling strategies with emphasis on response surface techniques. Applications included design of plates with discontinuities subject to uncertainty in material properties and geometry, design of stiffened composite plates for improved damage tolerance, and the use of response surfaces for fitting weights obtained by structural optimization.

Haftka, Raphael T.↗

Open-source Numerical Modeling of Solidification Cracking Susceptibility: Application to Refractory Alloy Systems

Introduction. Alloys such as aluminum, nickel-base, and austenitic stainless steels are susceptible to solidification cracking during welding and 3D printing. Compositional optimization is one method used to effectively mitigate solidification cracking of those alloy systems. With the surge in hypersonic and in-space propulsion activities, refractory metals (Nb, Mo, Ta, W, and Re) and their alloy derivatives are increasing in importance due to their extreme high melting point and retention of high-temperature strength; however, their chemistry was most typically optimized to promote ductility during mechanical operations such as drawing and forming. Welding of such alloys has been a challenge due to a number of issues including solidification cracking, atmospheric contamination (O, C, and N), as well as a shift in ductile-to-brittle transition to higher temperature following grain growth induced by welding. Compositional optimization of refractory alloys for solidification cracking resistance in particular is desirable as their usage increases with the advent of advanced manufacturing methods such as 3D printing. This work evaluates the effect of compositional variation in refractory metal systems on the solidification cracking susceptibility with the goals of optimizing existing alloys and joining process techniques, and formulating new alloys with increased solidification cracking resistance. Experimental Procedures. A python code was developed in a Jupyter notebook environment (Michael and Sowards, 2023) to facilitate the calculation of crack susceptibility index proposed by Kou (2015). Composition is entered as a single point, or as a 1-D or 2-D array. The notebook calls pycalphad (Otis and Liu, 2017 and Bocklund et al, 2020) to calculate the evolution of fraction solid as a function of temperature (under either Scheil or equilibrium assumptions) and then evaluates steepness of the fraction solid curve near the terminal stage of solidification to predict solidification cracking resistance. Open source thermodynamic databases available at online repositories are used (van de Walle). The process is setup in an automated fashion to generate plots that show variation in solidification cracking susceptibility according to composition on 1-D line plots or 2-D contour plots. The Jupyter notebook and crack susceptibility algorithm was also integrated with a widely used commercial CALPHAD code for validation and alloy exploration. Results and Discussion. The crack susceptibility model was first validated against a series of refractory alloy compositions evaluated in past work which utilized a specialized Varestraint test built inside a vacuum chamber environment (Lessman and Gold, 1971). The alloys tested in the Varestraint apparatus included T-111 (Ta-8W-2Hf), ASTAR-811C (Ta-8W-1Re-0.7Hf-0.025C), FS-85 (Nb-27Ta-10W-1Zr), T-222 (Ta-9.6W-2.4Hf-0.01C), Ta-10W, B-66 (Nb-5Mo-5V-1Zr), and SCb-291 (Nb-10W-10Ta). The initial test of the model showed a strong correlation with empirical Varestraint data, i.e., a Spearman rank correlation between model predictions and hot cracking measurements was observed to be greater than 0.8. Following the validation, a set of refractory metal binary mixtures was investigated to evaluate sensitivity of Nb, Mo, W, and Ta to C, N, and O content. A series of plots were produced that suggest ppmw ranges of C, N, and O where solidification cracking increases significantly and reaches a maximum. Also comparative ranking of each primary refractory metal to each interstitial was produced. For example C produces greater cracking response in Mo whereas O produces greater cracking response in Ta and Nb. Such compositional values have utility in setting limits on pickup of these interstitial elements during welding and printing rather than using a one-size-fits-all approach. Furthermore, the results have use in determining additive powder recycling requirements, which is especially pertinent for refractory metal powders due to their high cost compared to conventional alloys. Another application created thousands of hypothetical alloys within the nominal specified composition range of two widely used refractory alloys C103 (Nb-10Hf-1Ti) and TZM (Mo-0.5Ti-0.1Zr). The cracking index was calculated for the alloys and results were fed into machine learning regression techniques including Multiple Linear Regression, Ridge Regression, and Lasso Regression to determine relative potency each alloying element had on computed solidification cracking index. A series of linear equations were produced that relate composition of C103 and TZM to solidification cracking index. The crack susceptibility of C103 for example is described by an equation of the form: cracking index ~ O + 0.667*C + 0.635*N + 0.00037*Ta – 0.0008*Hf (in wt.%) From that equation, it is clear that O has strong propensity to induce solidification cracking. Interestingly, Hf is shown to reduce calculated cracking response. Finally, realizing the potential of this method to discover new refractory alloy formulations across the period table that have low solidification cracking sensitivity, the code was applied to new untested alloy systems including W-Zr-C, W-Ta-C, and others. Conclusions. In summary, an open source numerical method has been developed using Python code to calculate Kou’s crack susceptibility index. The method was applied to refractory metals which are inherently difficult to study from a weldability testing standpoint since inert shielding gas is not sufficient and welding is typically done in vacuum, especially in light of findings presented here where oxygen has profound influence on solidification cracking. This work revealed the effect of compositional variations on a series of refractory metals and showed the framework defined here will be useful in 1) the development of new alloys that have improved weldability and 3D printability, 2) placing compositional limits on existing alloys, and 3) ensuring adequate controls of manufacturing processes such as 3D printing where powder reuse is critical. Keywords. pycalphad; Python; refractory metals; solidification cracking. References. B. Bocklund et. al. (2020) http://doi.org/10.5281/zenodo.3630657. S. Kou. (2015) https://doi.org/10.1016/j.actamat.2015.01.034. G.G. Lessmann and R.E. Gold. Welding Journal, issue 1, pp. 1-s – 8-s (1971). F.N. Michael and J.W. Sowards. NASA/TM-20230002218 (2023). R. Otis and Z.-K. Liu. (2017) http://doi.org/10.5334/jors.140. A. Van de Wallle et. al. (2018) https://doi.org/10.1016/j.calphad.2018.04.003.

pycalphad↗

Optimization of composite box-beam structures including effects of subcomponent interactions

Minimum mass designs are obtained for a simple box beam structure subject to bending, torque and combined bending/torque load cases. These designs are obtained subject to point strain and linear buckling constraints. The present work differs from previous efforts in that special attention is payed to including the effects of subcomponent panel interaction in the optimal design process. Two different approaches are used to impose the buckling constraints. When the global approach is used, buckling constraints are imposed on the global structure via a linear eigenvalue analysis. This approach allows the subcomponent panels to interact in a realistic manner. The results obtained using this approach are compared to results obtained using a traditional, less expensive approach, called the local approach. When the local approach is used, in-plane loads are extracted from the global model and used to impose buckling constraints on each subcomponent panel individually. In the global cases, it is found that there can be significant interaction between skin, spar, and rib design variables. This coupling is weak or nonexistent in the local designs. It is determined that weight savings of up to 7% may be obtained by using the global approach instead of the local approach to design these structures. Several of the designs obtained using the linear buckling analysis are subjected to a geometrically nonlinear analysis. For the designs which were subjected to bending loads, the innermost rib panel begins to collapse at less than half the intended design load and in a mode different from that predicted by linear analysis. The discrepancy between the predicted linear and nonlinear responses is attributed to the effects of the nonlinear rib crushing load, and the parameter which controls this rib collapse failure mode is shown to be the rib thickness. The rib collapse failure mode may be avoided by increasing the rib thickness above the value obtained from the (linear analysis based) optimizer. It is concluded that it would be necessary to include geometric nonlinearities in the design optimization process if the true optimum in this case were to be found.

Ragon, Scott A.↗

A new sensitivity analysis for structural optimization of composite rotor blades

This paper presents a detailed mathematical derivation of the sensitivity derivatives for the structural dynamic, aeroelastic stability and response characteristics of a rotor blade in hover and forward flight. The formulation is denoted by the term semianalytical approach, because certain derivatives have to be evaluated by a finite difference scheme. Using the present formulation, sensitivity derivatives for the structural dynamic and aeroelastic stability characteristics, were evaluated for both isotropic and composite rotor blades. Based on the results, useful conclusions are obtained regarding the relative merits of the semi-analytical approach, for calculating sensitivity derivatives, when compared to a pure finite difference approach.

Venkatesan, C.↗

Tailoring of composite links for optimal damped elasto-dynamic performance

A method is developed for the optimal design of composite links based on dynamic performance criteria directly related to structural modal damping and dynamic stiffness. An integrated mechanics theory correlates structural composite damping to the parameters of basic composite material systems, laminate parameters, link shape, and modal deformations. The inclusion of modal properties allows the selective minimization of vibrations associated with specific modes. Ply angles and fiber volumes are tailored to obtain optimal combinations of damping and stiffness. Applications to simple composite links indicate wide margins for trade-offs and illustrate the importance of various design variables to the optimal design.

Saravanos, D. A.↗

Tailoring of composite links for optimal damped elasto-dynamic performance

A method is developed for the optimal design of composite links based on dynamic performance criteria directly related to structural modal damping and dynamic stiffness. An integrated mechanics theory correlates structural composite damping to the parameters of basic composite material systems, laminate parameters, link shape, and modal deformations. The inclusion of modal properties allows the selective minimization of vibrations associated with specific modes. Ply angles and fiber volumes are tailored to obtain optimal combinations of damping and stiffness. Applications to simple composite links indicate wide margins for trade-offs and illustrate the importance of various design variables to the optimal design.

Saravanos, D. A.↗

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.

Pai, Shantaram S.↗