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NASA NTRS1985

Finite Element Prediction of Loss Factors for Structures with Frequency-dependent Damping Treatments

A finite element procedure is described for calculating the loss factors for elastic structures to which frequency-dependent viscoelastic damping treatments were applied. The frequency dependence of the viscoelastic damping material is treated by approximating its shear modulus with a second-order polynomial so that the stiffnesses associated with the constant, linear, and quadratic terms can be combined, respectively, with the stiffness, damping, and mass matrices assembled for the rest of the structure. A single complex eigenvalue analysis is then performed in which the eigenvalues are purely imaginary. The loss factor is computed by the modal strain energy (MSE) approach. In the the MSE approach, the loss factor of a composite structure vibrating in one of its natural modes may be visualized as a weighted average of the loss factors of the component parts, with the relative stored energies as weighting constants. The finite element procedure, which can treat very general geometries, is illustrated for the case of a vibrating constrained-layer damped plate.

Everstine, G. C.↗

NASA NTRS1995

Contact Stress Analysis of Spiral Bevel Gears Using Finite Element Analysis

A procedure is presented for performing three-dimensional stress analysis of spiral bevel gears in mesh using the finite element method. The procedure involves generating a finite element model by solving equations that identify tooth surface coordinates. Coordinate transformations are used to orientate the gear and pinion for gear meshing. Contact boundary conditions are simulated with gap elements. A solution technique for correct orientation of the gap elements is given. Example models and results are presented.

Bibel, G. D.↗

NASA NTRS2002

Finite Element Modeling of the NASA Langley Aluminum Testbed Cylinder

The NASA Langley Aluminum Testbed Cylinder (ATC) was designed to serve as a universal structure for evaluating structural acoustic codes, modeling techniques and optimization methods used in the prediction of aircraft interior noise. Finite element models were developed for the components of the ATC based on the geometric, structural and material properties of the physical test structure. Numerically predicted modal frequencies for the longitudinal stringer, ring frame and dome component models, and six assembled ATC configurations were compared with experimental modal survey data. The finite element models were updated and refined, using physical parameters, to increase correlation with the measured modal data. Excellent agreement, within an average 1.5% to 2.9%, was obtained between the predicted and measured modal frequencies of the stringer, frame and dome components. The predictions for the modal frequencies of the assembled component Configurations I through V were within an average 2.9% and 9.1%. Finite element modal analyses were performed for comparison with 3 psi and 6 psi internal pressurization conditions in Configuration VI. The modal frequencies were predicted by applying differential stiffness to the elements with pressure loading and creating reduced matrices for beam elements with offsets inside external superelements. The average disagreement between the measured and predicted differences for the 0 psi and 6 psi internal pressure conditions was less than 0.5%. Comparably good agreement was obtained for the differences between the 0 psi and 3 psi measured and predicted internal pressure conditions.

Grosveld, Ferdinand W.↗

NASA NTRS1986

Computational solid mechanics (finite elements and boundary elements) - Present status and future directions

Computational finite-element and boundary-element methods are reviewed, and their application to the mechanics of solids is discussed. Stability conditions for general FEMs are considered in addition to the use of least-order, stable, invariant, or hybrid/mixed isoparametric elements as alternatives to the displacement-based isoparametric elements. The use of symbolic manipulation, adaptive mesh refinement, transient dynamic response, and boundary-element methods for linear elaslticity and finite-strain problems of inelastic materials are also discussed.

Atluri, S. N.↗

DOE OSTI2016

Finite element formulation of fluctuating hydrodynamics for fluids filled with rigid particles using boundary fitted meshes

In this paper, we present a finite element implementation of fluctuating hydrodynamics with a moving boundary fitted mesh for treating the suspended particles. The thermal fluctuations are incorporated into the continuum equations using the Landau and Lifshitz approach [1]. The proposed implementation fulfills the fluctuation–dissipation theorem exactly at the discrete level. Since we restrict the equations to the creeping flow case, this takes the form of a relation between the diffusion coefficient matrix and friction matrix both at the particle and nodal level of the finite elements. Brownian motion of arbitrarily shaped particles in complex confinements can be considered within the present formulation. A multi-step time integration scheme is developed to correctly capture the drift term required in the stochastic differential equation (SDE) describing the evolution of the positions of the particles. The proposed approach is validated by simulating the Brownian motion of a sphere between two parallel plates and the motion of a spherical particle in a cylindrical cavity. The time integration algorithm and the fluctuating hydrodynamics implementation are then applied to study the diffusion and the equilibrium probability distribution of a confined circle under an external harmonic potential.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS1991

A general purpose nonlinear rigid body mass finite element for application to rotary wing dynamics

The Second Generation Comprehensive Helicopter Analysis System employs the present formulation of the general-purpose nonlinear rigid body mass finite element, which represents the hub masses, blade tip masses, and pendulum vibration absorbers. The rigid body mass element has six degrees of freedom, and accounts for gravitational as well as dynamic effects. A consequence of deriving the element's equations from various physical principles is that, prior to the transformation which couples the rigid body mass element to the rotor blade finite element, the forces obtained for each element are fundamentally different; this is true notwithstanding the degrees-of-freedom of each element are parameterized using the same coordinates.

Hamilton, B. K.↗

DOE OSTI2022

A flexible linear diffusion acceleration to k-eigenvalue neutron transport with SN discontinuous finite element method

In this paper, we derive a flexible linear diffusion acceleration (LDA) for k-eigenvalue neutron transport discretized with discontinuous finite element method (DFEM) and discrete ordinates(SN). This LDA is based on our two pieces of previous works: the flexible non linear diffusion acceleration (NDA) for DFEM-SN and LDA for k-eigenvalue neutron transport using pre-conditioned Jacobian-free Newton-Krylov with self-adjoint angular flux (SAAF), continuous finite element method(CFEM), and SN. We point out the differences between LDA and NDA for DFEM-SN and the difference between DFEM-SN and SAAF-CFEM-SN for LDA. Numerical tests are presented to compare the convergence behaviour of NDA and LDA. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2023

Finite element modeling of biomass hopper flow

Hoppers are widely used biomass handling devices that channel bulk biomass from storage to subsequent handling equipment. Jenike’s longstanding approach, based on the Mohr-Coulomb model, has been successfully used to design hoppers handling cohesionless granular materials such as grains and other agricultural produces. However, designing a hopper to ensure reliable biomass flow is found to be challenging due to cohesion, irregular particle shape, and bulk material elastoplasticity. This study aims to address the biomass handling engineering challenge with alternative constitutive material models concerning the flow behavior of bulk solids. Finite element modeling is an approach that allows for implementation of different material models, whose underlying constitutive theories assist in investigating the origin and manifestation of bulk mechanical behavior of granular materials. This study focuses on the incipient gravity hopper flow of two types of biomass feedstocks, i.e., ground corn stover and Douglas fir wood. Three widely used constitutive material models, i.e., Mohr-Coulomb model, modified Cam-Clay model, and Drucker-Prager/Cap model, are implemented. Using the flow pattern represented by the volume of biomass exhibiting more than 7% of axial strain (Kamath and Puri, 1999), the finite element model predicts that the bulk corn stover particulate material forms an arch, which represents a hampered transition from the static state to the dynamic flow-state out of the hopper, whereas bulk Douglas fir wood particulate material develops a reliable mass flow pattern. A laboratory scale hopper was used to experimentally determine the biomass flow conditions, which were subsequently compared with the predicted onset of flow by a finite element model (FEM). The developed FEM was found to correctly predict the initiation of mass flow for the milled Douglas fir wood, whereas corn stover was predicted to establish a strong core flow suggesting an unreliable handling characteristic. This observation aligns with the reported poor handling of milled corn stover.

09 BIOMASS FUELS↗

NASA NTRS1990

Transient finite element computations on the transputer system

The aim was to study the solution of transient finite element problems on the Transputer system of parallel processors. The central difference time integration rule was used so that no equation solving was necessary. Also investigated was subcycling time integration which uses different time steps in different subdomains of the finite element mesh. A one-dimensional bar problem was analyzed using the parallel time integration algorithm. This involves subdividing the bar into subproblems which are assigned to different processors. Results show that the significant speed-up can be obtained through parallel processing. Also subcycling can give an additional speed-up in certain classes of problems. A two-dimensional problem was also examined to evaluate the effect of the communication to computation ratio on solution time.

Smolinski, Patrick J.↗

NASA NTRS1996

Development of Finite Elements for Two-Dimensional Structural Analysis Using the Integrated Force Method

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 configurations are presented. The element equilibrium and flexibility matrices are derived by discretizing the expressions for potential and complementary energies, respectively. The displacement and stress fields within the finite elements are independently approximated. The displacement field is interpolated as it is in the standard displacement method, and the stress field is approximated by using complete polynomials of the correct order. A procedure that uses the definitions of stress components in terms of an Airy stress function is developed to derive the stress interpolation polynomials. Such derived stress fields identically satisfy the equations of equilibrium. Moreover, the resulting element matrices are insensitive to the orientation of local coordinate systems. A method is devised to calculate the number of rigid body modes, and the present elements are shown to be free of spurious zero-energy modes. A number of example problems are solved by using the present library, and the results are compared with corresponding analytical solutions and with results from the standard displacement finite element method. The Integrated Force Method not only gives results that agree well with analytical and displacement method results but also outperforms the displacement method in stress calculations.

Kaljevic, Igor↗

NASA NTRS1976

TAP 1: A Finite Element Program for Steady-State Thermal Analysis of Convectively Cooled Structures

The program has a finite element library of six elements: two conduction/convection elements to model heat transfer in a solid, two convection elements to model heat transfer in a fluid, and two integrated conduction/convection elements to represent combined heat transfer in tubular and plate/fin fluid passages. Nonlinear thermal analysis due to temperature dependent thermal parameters is performed using the Newton-Raphson iteration method. Program output includes nodal temperatures and element heat fluxes. Pressure drops in fluid passages may be computed as an option. A companion plotting program for displaying the finite element model and predicted temperature distributions is presented. User instructions and sample problems are presented in appendixes.

Thornton, E. A.↗

NASA NTRS1993

Contact stress analysis of spiral bevel gears using nonlinear finite element static analysis

Bibel, G. D.↗

NASA NTRS1993

Contact stress analysis of spiral bevel gears using nonlinear finite element static analysis

Bibel, G. D.↗

NASA NTRS1994

Using Finite-Element Analysis In Estimating Reliability

Method of estimating design survivability of structural component incorporates finite-element and probabilistic properties of materials. Involves evaluation of design parameters through direct comparisons of survivability of component expressed in terms of percentages of like components that survive at various lifetimes. Probabilistic properties of materials, given in terms of Weibull parameters, coupled with stress field computed by finite-element analysis to determine fatigue life based on initiation of cracks. Method applied to rotating disk containing bolt holes, representative of disks used in aerospace propulsion turbines. Also used in early stages of design process to optimize life-based designs, reducing testing of full-sized components needed to validate designs.

Zaretsky, Erwin V.↗

NASA NTRS1981

Free-Vibration Analysis of Rotating Beams by a Variable-Order Finite-Element Method

The free vibration of rotating beams is analyzed by means of a finite-element method of variable order. This method entails displacement functions that are a complete power series of a variable number of terms. The terms are arranged so that the generalized coordinates are composed of displacements and slopes at the element extremities and, additionally, displacements at certain points within the element. The displacement is assumed to be analytic within an element and thus can be approximated to any degree of accuracy desired by a complete power series. Numerical results are presented for uniform beams with zero and nonzero hub radii, tapered beams, and a nonuniform beam with discontinuities. Since the present method reduces to a conventional beam finite-element method for a cubic displacement function, the results are compared and found to be superior to the conventional results in terms of accuracy for a given number of degrees of freedom. Indeed, essentially exact eigenvalues and eigenvectors are obtained with this technique, which is far more rapidly convergent than other approaches in the literature.

Hodges, Dewey H.↗

DOE OSTI2019

Matrix-free subcell residual distribution for Bernstein finite element discretizations of linear advection equations

In this work, we introduce a new residual distribution (RD) framework for the design of bound-preserving high-resolution finite element schemes. The continuous and discontinuous Galerkin discretizations of the linear advection equation are modified to construct local extremum diminishing (LED) approximations. To that end, we perform mass lumping and redistribute the element residuals in a manner which guarantees the LED property. The hierarchical correction procedure for high-order Bernstein finite element discretizations involves localization to subcells and definition of bound-preserving weights for subcell contributions. Using strong stability preserving (SSP) Runge–Kutta methods for time integration, we prove the validity of discrete maximum principles under CFL-like time step restrictions. The low-order version of our method has roughly the same accuracy as the one derived from a piecewise (multi)-linear approximation on a submesh with the same nodal points. In high-order extensions, we use an element-based flux-corrected transport (FCT) algorithm which can be interpreted as a nonlinear RD scheme. The proposed LED corrections are tailor-made for matrix-free implementations which avoid the rapidly growing cost of matrix assembly for high-order Bernstein elements. The results for 1D, 2D, and 3D test problems compare favorably to those obtained with the best matrix-based approaches.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1976

Application of finite element approach to transonic flow problems

A variational finite element model for transonic small disturbance calculations is described. Different strategy is adopted in subsonic and supersonic regions, and blending elements are introduced between different regions. In the supersonic region, no upstream effect is allowed. If rectangular elements with linear shape functions are used, the model is similar to Murman's finite difference operators. Higher order shape functions, nonrectangular elements, and discontinuous approximation of shock waves are also discussed.

Hafez, M. M.↗

NASA NTRS1991

STARS: An integrated general-purpose finite element structural, aeroelastic, and aeroservoelastic analysis computer program

The details of an integrated general-purpose finite element structural analysis computer program which is also capable of solving complex multidisciplinary problems is presented. Thus, the SOLIDS module of the program possesses an extensive finite element library suitable for modeling most practical problems and is capable of solving statics, vibration, buckling, and dynamic response problems of complex structures, including spinning ones. The aerodynamic module, AERO, enables computation of unsteady aerodynamic forces for both subsonic and supersonic flow for subsequent flutter and divergence analysis of the structure. The associated aeroservoelastic analysis module, ASE, effects aero-structural-control stability analysis yielding frequency responses as well as damping characteristics of the structure. The program is written in standard FORTRAN to run on a wide variety of computers. Extensive graphics, preprocessing, and postprocessing routines are also available pertaining to a number of terminals.

Gupta, Kajal K.↗