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At least 289 records · Page 16

Extremized nonlinear and linearized responses in soft metamaterials enabled by gradient-based design and grayscale digital light processing

In this study, we develop a gradient-based design approach that exploits grayscale digital light processing (DLP) 3D printing for extremizing the nonlinear and linearized response of soft metamaterials — materials that harness engineered geometric instabilities to undergo large and programmable changes in configuration. Grayscale DLP approaches modulate local mechanical properties at the pixel scale by tuning the light intensity within a single grayscale image, unlocking an exceptionally large design space. To effectively navigate this space, we develop smooth mappings between local light intensity values and global quantities of interest that characterize the behavior of soft metamaterials. Enabling these smooth mappings are robust and differentiable nonlinear finite element simulations powered by a trust region solver. A PDE-constrained optimization problem is then solved to invert these mappings and produce light intensity distributions that endow the printed part with varying stiffness and flexibility in distinctive regions. It is shown that optimizing the distribution of soft and stiff phases throughout a metamaterial structure results in markedly different buckling and self-contact configurations to drive extremized nonlinear compression and linearized vibration responses. Optimized light intensity distributions are translated to grayscale images and directly used to print soft metamaterial samples, showing remarkable agreement between the buckling and self-contact response in simulated and measured deformed configurations.

Additive manufacturing↗

Long fluid filled bags suspended by line forces

A previous analysis of fluid filled storage bags is extended to the case of a long fluid filled cylindrical membrane supported by uniform line loads. Cross-sectional shape, stiffness of the support system and stress resultants in the membrane are determined. The application of the numerical results to problems arising in the design of nonrigid airships is discussed.

Mullins, M. L.↗

Application of the aerodynamic energy concept to the selection of transfer functions for flutter suppression and gust alleviation using active controls

Changes are introduced in the aerodynamic energy approach which lead to an increase in the effectiveness of both the trailing-edge (TE) and the leading-edge (LE)-TE control systems. Control laws are determined, using realizable transfer functions, which permit the introduction of aerodynamic damping and stiffness terms in accordance with the requirements of any specific system. It is shown that flutter suppression and gust alleviation problems can successfully be treated either by a TE or by a LE-TE control system. The results obtained are applicable to a very wide class of aircraft operating within the subsonic Mach number range.

Nissim, E.↗

The buckling of a column on equally spaced deflectional and rotational springs

A solution is presented for the problem of the buckling of a column on equally spaced deflectional and rotational springs. Useful charts, which relate deflectional spring stiffness, rotational spring stiffness, and buckling load, are given for columns having two, three, four, and infinite number of spans.

FORMULAS - BUCKLING↗

A Gas-Kinetic Method for Hyperbolic-Elliptic Equations and Its Application in Two-Phase Fluid Flow

A gas-kinetic method for the hyperbolic-elliptic equations is presented in this paper. In the mixed type system, the co-existence and the phase transition between liquid and gas are described by the van der Waals-type equation of state (EOS). Due to the unstable mechanism for a fluid in the elliptic region, interface between the liquid and gas can be kept sharp through the condensation and evaporation process to remove the "averaged" numerical fluid away from the elliptic region, and the interface thickness depends on the numerical diffusion and stiffness of the phase change. A few examples are presented in this paper for both phase transition and multifluid interface problems.

Xu, Kun↗

Multiphysics Time-Integration for Turbulent Combustion at the Exascale

Turbulent reacting flow systems are often modeled with coupled time-dependent partial differential equations (PDEs). Solving such equations can easily tax the world's largest supercomputers. One pragmatic strategy for attacking such problems is to split the PDEs into components that can more easily be solved in isolation. This generic operator-splitting strategy leads to a set of ordinary differential equations (ODEs) that need to be solved as part of an "outer-loop" time-stepping approach. In many combustion applications, the ODEs to be solved can be very stiff, exhibiting timescales that span many orders of magnitude. The SUNDIALS library provides a plethora of robust time integration algorithms for solving these ODEs on exascale-capable computing hardware, yet for many complex applications (such multicomponent fuels or emissions predictions), the chemical models remain too complex to solve using reasonable resources. The Quasi-Steady State Approximation (QSSA) can be an effective tool for reducing the size and stiffness of the simulations. In this talk, I will discuss the use of the SUDIALS library of ODE solvers together with automatic code generation tools to solve complex turbulent reacting flow problems using QSSA models.

chemistry↗

Parallel triangularization of substructured finite element problems

Much of the computational effort of the finite element process involves the solution of a system of linear equations. The coefficient matrix of this system, known as the global stiffness matrix, is symmetric, positive definite, and generally sparse. An important technique for reducing the time required to solve this system is substructuring or matrix partitioning. Substructuring is based on the idea of dividing a structure into pieces, each of which can then be analyzed relatively indepenently. As a result of this division, each point in the finite element discretization is either interior to a substructure or on a boundary between substructures. Contributions to the global stiffness matrix from connections between boundary points from the K(bb) matrix are reported. The triangularization of a general K(bb) matrix on a parallel machine is specifically discussed.

Leuze, M. R.↗

Enhancements to Sperry/NASTRAN

Reviewed is the enhancement to NASTRAN program performed by NUK (Nippon Univac Kaisha, Ltd.) added to Level 15.5. Features discussed include intermediate checkpoint-restart in triangular decomposition, I/O improvement, multibanked memory and new plate element. The first three improvements provide the capability to solve significantly large size problems, while the new elements release the analyst from the cumbersome work to constrain the singularities caused by the lack of stiffness of inplane rotation of old plate elements.

Koga, T.↗

A perturbation technique for parameter identification in distributed structures

Structures are often characterized by parameters, such as mass and stiffness, that are spatially distributed. Parameter identification of distributed structures is subject to many of the difficulties involved in the modeling problem, and the choice of the model can greatly affect the results of the parameter identification process. Analogously to control spillover in the control of distributed-parameter systems, identification spillover is shown to exist as well and its effect is to degrade the parameter estimates. Moreover, as in modeling by the Rayleigh-Ritz method, it is shown that, for a Rayleigh-Ritz type identification algorithm, an inclusion principle exists in the identification of distributed-parameter systems as well, so that the identified natural frequencies approach the actual natural frequencies monotonically from above.

Meirovitch, L.↗

A proposed method for enhanced eigen-pair extraction using finite element methods: Theory and application

The paper covers two distinct parts: theory and application. The goal of this work was the reduction of model size with an increase in eigenvalue/vector accuracy. This method is ideal for the condensation of large truss- or beam-type structures. The theoretical approach involves the conversion of a continuum transfer matrix beam element into an 'Exact' dynamic stiffness element. This formulation is implemented in a finite element environment. This results in the need to solve a transcendental eigenvalue problem. Once the eigenvalue is determined the eigenvectors can be reconstructed with any desired spatial precision. No discretization limitations are imposed on the reconstruction. The results of such a combined finite element and transfer matrix formulation is a much smaller FEM eigenvalue problem. This formulation has the ability to extract higher eigenvalues as easily and as accurately as lower eigenvalues. Moreover, one can extract many more eigenvalues/vectors from the model than the number of degrees of freedom in the FEM formulation. Typically, the number of eigenvalues accurately extractable via the 'Exact' element method are at least 8 times the number of degrees of freedom. In contrast, the FEM usually extracts one accurate (within 5 percent) eigenvalue for each 3-4 degrees of freedom. The 'Exact' element results in a 20-30 improvement in the number of accurately extractable eigenvalues and eigenvectors.

Jara-Almonte, J.↗

Modeling of Structural-Acoustic Interaction Using Coupled FE/BE Method and Control of Interior Acoustic Pressure Using Piezoelectric Actuators

A coupled finite element (FE) and boundary element (BE) approach is presented to model full coupled structural/acoustic/piezoelectric systems. The dual reciprocity boundary element method is used so that the natural frequencies and mode shapes of the coupled system can be obtained, and to extend this approach to time dependent problems. The boundary element method is applied to interior acoustic domains, and the results are very accurate when compared with limited exact solutions. Structural-acoustic problems are then analyzed with the coupled finite element/boundary element method, where the finite element method models the structural domain and the boundary element method models the acoustic domain. Results for a system consisting of an isotropic panel and a cubic cavity are in good agreement with exact solutions and experiment data. The response of a composite panel backed cavity is then obtained. The results show that the mass and stiffness of piezoelectric layers have to be considered. The coupled finite element and boundary element equations are transformed into modal coordinates, which is more convenient for transient excitation. Several transient problems are solved based on this formulation. Two control designs, a linear quadratic regulator (LQR) and a feedforward controller, are applied to reduce the acoustic pressure inside the cavity based on the equations in modal coordinates. The results indicate that both controllers can reduce the interior acoustic pressure and the plate deflection.

Mei, Chuh↗

The Role of Radial Clearance on the Performance of Foil Air Bearings

Load capacity tests were conducted to determine how radial clearance variations affect the load capacity coefficient of foil air bearings. Two Generation III foil air bearings with the same design but possessing different initial radial clearances were tested at room temperature against an as-ground PS304 coated journal operating at 30,000 rpm. Increases in radial clearance were accomplished by reducing the journal's outside diameter via an in-place grinding system. From each load capacity test the bearing load capacity coefficient was calculated from the rule-of-thumb (ROT) model developed for foil air bearings. The test results indicate that, in terms of the load capacity coefficient, radial clearance has a direct impact on the performance of the foil air bearing. Each test bearing exhibited an optimum radial clearance that resulted in a maximum load capacity coefficient. Relative to this optimum value are two separate operating regimes that are governed by different modes of failure. Bearings operating with radial clearances less than the optimum exhibit load capacity coefficients that are a strong function of radial clearance and are prone to a thermal runaway failure mechanism and bearing seizure. Conversely, a bearing operating with a radial clearance twice the optimum suffered only a 20 percent decline in its maximum load capacity coefficient and did not experience any thermal management problems. However, it is unknown to what degree these changes in radial clearance had on other performance parameters, such as the stiffness and damping properties of the bearings.

Radil, Kevin↗

Transverse cracking and stiffness reduction in composite laminates

A study of transverse cracking mechanism in composite laminates is presented using a singular hybrid finite element model. The model provides the global structural response as well as the precise local crack-tip stress fields. An elasticity basis for the problem is established by employing Lekhnitskii's complex variable potentials and method of eigenfunction expansion. Stress singularities associated with the transverse crack are obtained by decomposing the deformation into the symmetric and antisymmetric modes and proper boundary conditions. A singular hybrid element is thereby formulated based on the variational principle of a modified hybrid functional to incorporate local crack singularities. Axial stiffness reduction due to transverse cracking is studied. The results are shown to be in very good agreement with the existing experimental data. Comparison with simple shear lag analysis is also given. The effects of stress intensity factors and strain energy density on the increase of crack density are analyzed. The results reveal that the parameters approach definite limits when crack densities are saturated, an evidence of the existence of characteristic damage state.

Yuan, F. G.↗

An efficient, conservative, time-implicit solver for the fully kinetic arbitrary-species 1D-2V Vlasov-Ampère system

In this paper, we consider the solution of the fully kinetic (including electrons) Vlasov-Ampère system in a one-dimensional physical space and two-dimensional velocity space (1D-2V) for an arbitrary number of species with a time-implicit Eulerian algorithm. The problem of velocity-space meshing for disparate thermal and bulk velocities is dealt with by an adaptive coordinate transformation of the Vlasov equation for each species, which is then discretized, including the resulting inertial terms. Mass, momentum, and energy are conserved, and Gauss's law is enforced to within the nonlinear convergence tolerance of the iterative solver through a set of nonlinear constraint functions while permitting significant flexibility in choosing discretizations in time, configuration, and velocity space. We mitigate the temporal stiffness introduced by, e.g., the plasma frequency through the use of high-order/low-order (HOLO) acceleration of the iterative implicit solver. We present several numerical results for canonical problems of varying degrees of complexity, including the multiscale ion-acoustic shock wave problem, which demonstrate the efficacy, accuracy, and efficiency of the scheme.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASTRAN implementation of an isoparametric doubly-curved quadrilateral shell element

A quadrilateral shell element, CQUAD4, was added to level 15.5 and subsequently to level 16.0 of NASTRAN. The element exhibited doubly curved surfaces and used biquadratic interpolation functions. Reduced integration techniques were used to improve the performance of the element in thin shell problems. The creation of several new bulk data items is discussed, along with a special module, GPNORM, to process SHLNORM bulk data cards. In addition to the theoretical basis for the element stiffness matrix, consistent mass and load matrices are presented. Several potential sources of degenerate behavior of the element were investigated. Guidelines for proper use of the element were suggested. Performance of the element on several widely published classical examples was demonstrated. The results showed a significant improvement over presently available NASTRAN shell elements for even the coarsest meshes. Potential applications to two classes of practical problems are discussed.

Potvin, A. B.↗

Regal Beloit Final Technical Report

The original project proposal submitted from NovaTorque Inc (NovaTorque) in 2016 was to improve the existing motor with 95% efficiency by reducing the losses by 21% to achieve 96%. A few months after the proposal was submitted, NovaTorque lost funding and went out of business. The assets of NovaTorque were then acquired by Regal Beloit Corporation (“Regal Beloit” or “Regal”). When the NovaTorque proposal was selected, the project was transferred to Regal Beloit. Once we had production samples from the new Regal production line, they were tested at the Regal Beloit test lab in Wausau, WI. The original NovaTorque motor had an efficiency of 95%, but when the technology was transferred to Regal Beloit, there were multiple manufacturing improvements made, even though the basic electromagnetic design did not change. The test results in Wausau showed that the motors made at the Regal Beloit plant had an efficiency of 96%. Since the goal of the project was to reduce the losses by 21%, a new efficiency target of 96.8% became the project objective. In the first budget period, motors were tested to get the baseline performance. We then used FEA modeling with ANSYS Maxwell to model the existing motor to get correlation between the FEA simulations and the actual test results. Once the model was validated, we evaluated some changes that could be made to the stator to reduce the losses and improve efficiency without changing the rotor or stator housing, keeping the modifications easy to implement. The changes were primarily in the area of making the stator axially shorter and adding Soft Magnetic Composite (SMC) tooth tips. In the second budget period, we proceeded to design and build the new stator that was identified above and identified additional improvements in the process that included a stator machining modification and the use of rectangular wire. When we actually built the motor, the choice of rectangular wire turned out to be a problem. The wire was made by squishing round wire to get the rectangular shape, which caused work hardening, making the wire too stiff to make the desired coils. We shifted to annealed square wire which was better, but we still could not maintain the proper coil envelope. The result was that we had reduced cross section area for stator laminations. We also had to have a radial offset resulting in a radial misalignment between the stator and rotor because of the oversized coils. After the motor was completed, it was shipped to Texas A&M University for testing. With the loss of flux from these issues, the measured motor efficiency was only 96.3%. The primary focus of this motor was to make sure our FEA simulation model predicted the measured losses and overall efficiency, this we moved on to the FEA simulation. The FEA simulations of the motor “as built” with misalignments had good correlation with the test results, so the next step was to use that model to optimize the design of the motor for a final build. This time we considered changes to the stator and rotor and also minor changes to the housing diameter. In the third budget period, we did the detailed design and construction of the final prototypes. The final prototypes had a slight increase in the stator diameter to fit in a standard Regal Beloit housing. We shortened the stator and use more layers of wire in the coils. We also increased the cone angle of the rotor and stator from the original 110 degrees to 130 degrees to get some additional efficiency and optimized the stator cross section. The predicted efficiency from the FEA simulations was 96.9%. When completed, the motors were tested. We were a little short of reaching our target efficiency goal of 96.8%. We were only able to get to 96.7% efficiency. While it may be possible with additional iterations in designs and future builds to gain that additional 0.1%, we believe that we are close to the best we can achieve from a practical viewpoint, and additional iterations would be more work than the potential gains would be worth. No other motor in this class can even reach the 96% that we started with.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Comparison of supercritical and conventional wing flutter characteristics

A wind-tunnel study was undertaken to directly compare the measured flutter boundaries of two dynamically similar aeroelastic models which had the same planform, maximum thickness-to-chord ratio, and as nearly identical stiffness and mass distributions as possible, with one wing having a supercritical airfoil and the other a conventional airfoil. The considerations and problems associated with flutter testing supercritical wing models at or near design lift coefficients are discussed, and the measured transonic boundaries of the two wings are compared with boundaries calculated with a subsonic lifting surface theory.

Farmer, M. G.↗

Application of the method of lines for solution of the Navier-Stokes equations using nonuniform grid distributions

The method of lines is investigated for the numerical solution of the stream function and velocity form of the Navier-Stokes equations on nonuniform grids. Stiffness characteristics of a linear one-dimensional model equation are examined to establish the feasibility of applying the method to the volicity equation in two dimensions. It is observed that the transformed governing equations in computational domain become stiffer with increasing the number of grid points and the differencing technique affects the stiffness characteristics. The results demonstrate that the method of lines under certain circumstances is highly suitable for the numerical solution of physical problems on domains covered with variable grids.

Tiwari, S. N.↗