Conservatism in the Structural Design Process Associated With Assuming Dynamic Loads are Static 2024
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Large scale nonlinear numerical optimal control for finite element models of flexible structures
This paper discusses the development of large scale numerical optimal control algorithms for nonlinear systems and their application to finite element models of structures. This work is based on our expansion of the optimal control algorithm (DDP) in the following steps: improvement of convergence for initial policies in non-convex regions, development of a numerically accurate penalty function method approach for constrained DDP problems, and parallel processing on supercomputers. The expanded constrained DDP algorithm was applied to the control of a four-bay, two dimensional truss with 12 soft members, which generates geometric nonlinearities. Using an explicit finite element model to describe the structural system requires 32 state variables and 10,000 time steps. Our numerical results indicate that for constrained or unconstrained structural problems with nonlinear dynamics, the results obtained by our expanded constrained DDP are significantly better than those obtained using linear-quadratic feedback control.
Shoemaker, Christine A.↗
Design for Manufacturing of Structures with Automated Fiber Placement via Integration of Analysis and Process Planning
Under the Design for Manufacturing (DFM) task in the NASA HiCAM program, significant process has been made towards establishing a fully automated optimization process that spans the structural analysis, design, and manufacturing process planning for Automated Fiber Placement (AFP) structures. Previous efforts in this area established the data formats and mapping processes needed to exchange data between disciplines. The software tools used in the framework are HyperX (structural optimization), CAPP (process planning), and VCP (AFP path generation). The work has culminated with automation of data exchanges and an optimization process that drives the three software toward convergence. Within this framework, HyperX is used to generate mass-optimum composite designs which are iterated with VCP and CAPP to improve manufacturability of the designs. As the ply manufacturing process is adjusted by CAPP and VCP, HyperX continually re-assesses the structural integrity of the part and makes adjustments to the laminate as needed. For example, the position of fiber steering and tow overlaps/gaps can necessitate changes to the laminate design. Once the design converges, the end result is a stack of plies that meets both structural and manufacturing requirements. This paper presents the details of the framework and demonstrations the automated process on several parts with significant double-curvature.
HiCAM↗
Parallel-vector computation for linear structural analysis and non-linear unconstrained optimization problems
Several parallel-vector computational improvements to the unconstrained optimization procedure are described which speed up the structural analysis-synthesis process. A fast parallel-vector Choleski-based equation solver, pvsolve, is incorporated into the well-known SAP-4 general-purpose finite-element code. The new code, denoted PV-SAP, is tested for static structural analysis. Initial results on a four processor CRAY 2 show that using pvsolve reduces the equation solution time by a factor of 14-16 over the original SAP-4 code. In addition, parallel-vector procedures for the Golden Block Search technique and the BFGS method are developed and tested for nonlinear unconstrained optimization. A parallel version of an iterative solver and the pvsolve direct solver are incorporated into the BFGS method. Preliminary results on nonlinear unconstrained optimization test problems, using pvsolve in the analysis, show excellent parallel-vector performance indicating that these parallel-vector algorithms can be used in a new generation of finite-element based structural design/analysis-synthesis codes.
Nguyen, D. T.↗
The dynamics and control of large flexible space structures - 13
The optimal control of three-dimensional large angle maneuvers and vibrations of a Shuttle-mast-reflector system is considered. The nonlinear equations of motion are formulated by using Lagrange's formula, with the mast modeled as a continuous beam subject to three-dimensional deformations. Pontryagin's Maximum Principle is applied to the slewing problem, to derive the necessary conditions for the optimal controls, which are bounded by given saturation levels. The resulting two point boundary value problem is then solved by using the quasilinearization algorithm and the method of particular solutions. The study of the large angle maneuvering of the Shuttle-beam-reflector spacecraft in the plane of a circular earth orbit is extended to consider the effects of the structural offset connection, the axial shortening, and the gravitational torque on the slewing motion. Finally the effect of additional design parameters (such as related to additional payload requirement) on the linear quadratic regulator based design of an orbiting control/structural system is examined.
Bainum, Peter M.↗
Optimal member damper controller design for large space structures
Consideration is given to the selection of velocity feedback gains for individual dampers for the members of a structurally controlled large flexible space structure. The problem is formulated as an optimal output feedback regulator problem, and necessary conditions are derived for minimizing a quadratic performance function. The diagonal nature of the gain matrix is taken into account, along with knowledge of noise covariances. It is pointed out that the method presented offers a systematic approach to the design of a class of controllers for enhancing structural damping, which have significant potential if used in conjunction with a reduced-order optimal controller for rigid-body modes and selected structural modes.
Joshi, S. M.↗
Road map to adaptive optimal control
A building block control structure leading toward adaptive, optimal control for jet engines is developed. This approach simplifies the addition of new features and allows for easier checkout of the control by providing a baseline system for comparison. Also, it is possible to eliminate certain features that do not have payoff by being selective in the addition of new building blocks to be added to the baseline system. The minimum risk approach specifically addresses the need for active identification of the plant to be controlled in real time and real time optimization of the control for the identified plant.
Boyer, R.↗
Closed-loop structural stability for linear-quadratic optimal systems
An explicit parametrization of a subclass of linear constant gain feedback maps that never destabilize an originally open-loop stable system is presented. These results are used to obtain several new structural stability results for multiinput linear-quadratic feedback optimal designs.
Wong, P. K.↗
Recent developments in equivalent plate modeling for wing shape optimization
A new technique for structural modeling of airplane wings is presented taking transverse shear effects into account. The kinematic assumptions of first order shear deformation plate theory in combination with numerical analysis based on simple polynomials which define geometry, construction and displacement approximations lead to analytical expressions for elements of the stiffness and mass matrices and load vector. Contributions from the cover skins, spar and rib caps and spar and rib webs are included as well as concentrated springs and concentrated masses. Limitations of current equivalent plate wing modeling techniques based on classical plate theory are discussed, and the improved accuracy of the new equivalent plate technique is demonstrated through comparison to finite element analysis and test results. Analytical derivatives of stiffness, mass and load terms with respect to wing shape lead to analytic sensitivities of displacements, stresses and natural modes with respect to planform shape and depth distribution. This makes the new capability an effective structural tool for wing shape optimization.
Livne, Eli↗
Structured-groove phase gratings for control and optimization of the spectral efficiency
Phase gratings are used as dispersers in a variety of imaging spectroscopic instruments. However, conventional phase gratings provide limited spectral range and flexibility to fully optimize instrument performance for challenging applications. Presented here is a new design method that tailors and optimizes the spectral efficiency by introducing an arbitrary structure into the grating groove profile.
diffraction gratings↗
Closed-loop structural stability for linear-quadratic optimal systems
This paper contains an explicit parametrization of a subclass of linear constant gain feedback maps that will not destabilize an originally open-loop stable system. These results can then be used to obtain several new structural stability results for multiinput linear-quadratic feedback optimal designs.
Wong, P. K.↗
Integrated Control with Structural Feedback to Enable Lightweight Aircraft
This presentation for the Fundamental Aeronautics Program Technical Conference covers the benefits of active structural control, related research areas, and focuses on the use of optimal control allocation for the prevention of critical loads. Active control of lightweight structures has the potential to reduce aircraft weight and fuel burn. Sensor, control law, materials, control effector, and system level research will be necessary to enable active control of lightweight structures. Optimal control allocation with structural feedback has been shown in simulation to be feasible in preventing critical loads and is one example of a control law to enable future lightweight aircraft.
Taylor, Brian R.↗
Design of structures for optimum geometry
A general method is proposed for geometric optimization of finite element structures on the assumption that a reasonable initial geometry is specified. The number of finite elements, number of joints, and the element-joint relationships are specified and are not changed during the optimization process. The structure may be statically indeterminate and may support multiple loading conditions. Design variables include geometric and member sizing parameters. Design objectives may be minimum weight or cost, and constraints include strength and stiffness limitations. The optimization procedure is a general mathematical programming approach. An iterative design algorithm is outlined, and the method is specialized for truss structures. Design examples are given.
Vanderplaats, G. N.↗
Closed-loop structural stability for linear-quadratic optimal systems
This paper contains an explicit parameterization of a subclass of linear constant gain feedback maps that never destabilize an originally open-loop stable system. These results can then be used to obtain several new structural stability results for multi-input linear-quadratic feedback optimal designs.
Wong, P. K.↗
Closed-loop structural stability for linear-quadratic optimal system
This paper contains an explicit parameterization of a subclass of linear constant gain feedback maps that will not destabilize an originally open-loop stable system. These results can then be used to obtain several new structural stability results for multi-input linear-quadratic feedback optimal designs.
Wong, P. K.↗
Closed-loop structural stability for linear-quadratic optimal systems
This paper contains an explicit parametrization of a subclass of linear constant gain feedback maps that will not destabilize an originally open-loop stable system. These results can then be used to obtain several new structural stability results for multi-input linear-quadratic feedback optimal designs.
Wong, P. K.↗
An optical fixed control structure design with minimal sensitivity for a large elastic booster
Optimal fixed control structure design with minimal sensitivity for large elastic booster
Dangelo, H.↗
A structural design decomposition method utilizing substructuring
A new method of design decomposition for structural analysis and optimization is described. For this method, the structure is divided into substructures where each substructure has its structural response described by a structural-response subproblem, and its structural sizing determined from a structural-sizing subproblem. The structural responses of substructures that have rigid body modes when separated from the remainder of the structure are further decomposed into displacements that have no rigid body components, and a set of rigid body modes. The structural-response subproblems are linked together through forces determined within a structural-sizing coordination subproblem which also determines the magnitude of any rigid body displacements. Structural-sizing subproblems having constraints local to the substructures are linked together through penalty terms that are determined by a structural-sizing coordination subproblem. All the substructure structural-response subproblems are totally decoupled from each other, as are all the substructure structural-sizing subproblems, thus there is significant potential for use of parallel solution methods for these subproblems.
Scotti, Stephen J.↗