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All sourcesNASA NTRSDOE OSTI
NASA NTRS2011

Damage Characterization Using the Extended Finite Element Method for Structural Health Management

The development of validated multidisciplinary Integrated Vehicle Health Management (IVHM) tools, technologies, and techniques to enable detection, diagnosis, prognosis, and mitigation in the presence of adverse conditions during flight will provide effective solutions to deal with safety related challenges facing next generation aircraft. The adverse conditions include loss of control caused by environmental factors, actuator and sensor faults or failures, and damage conditions. A major concern in these structures is the growth of undetected damage/cracks due to fatigue and low velocity foreign impact that can reach a critical size during flight, resulting in loss of control of the aircraft. Hence, development of efficient methodologies to determine the presence, location, and severity of damage/cracks in critical structural components is highly important in developing efficient structural health management systems.

Krishnamurthy, Thiagarajan↗
NASA NTRS2013

A Floating Node Method for the Modelling of Discontinuities Within a Finite Element

This paper focuses on the accurate numerical representation of complex networks of evolving discontinuities in solids, with particular emphasis on cracks. The limitation of the standard finite element method (FEM) in approximating discontinuous solutions has motivated the development of re-meshing, smeared crack models, the eXtended Finite Element Method (XFEM) and the Phantom Node Method (PNM). We propose a new method which has some similarities to the PNM, but crucially: (i) does not introduce an error on the crack geometry when mapping to natural coordinates; (ii) does not require numerical integration over only part of a domain; (iii) can incorporate weak discontinuities and cohesive cracks more readily; (iv) is ideally suited for the representation of multiple and complex networks of (weak, strong and cohesive) discontinuities; (v) leads to the same solution as a finite element mesh where the discontinuity is represented explicitly; and (vi) is conceptually simpler than the PNM.

Pinho, Silvestre T.↗
NASA NTRS2023

Modeling holes and voids in three dimensions using a single element within the Extended Finite Element framework

This paper introduces a highly efficient computational approach using the extended finite element method to model three-dimensional mechanics of holes and voids. The defect is encapsulated within a single element with a tailored exponential enrichment function that captures the behavior near the discontinuity boundary and can account for the pressure acting on the void’s surface through an equivalent nodal force vector. The method’s results were compared against analytical solutions and conventional finite element method results for problems involving single and multiple holes. The comparison demonstrated that the method provides accurate stress concentration estimates while adhering to computational constraints.

Adnan Shahriar↗
NASA NTRS1972

Finite elements of nonlinear continua.

The finite element method is extended to a broad class of practical nonlinear problems, treating both theory and applications from a general and unifying point of view. The thermomechanical principles of continuous media and the properties of the finite element method are outlined, and are brought together to produce discrete physical models of nonlinear continua. The mathematical properties of the models are analyzed, and the numerical solution of the equations governing the discrete models is examined. The application of the models to nonlinear problems in finite elasticity, viscoelasticity, heat conduction, and thermoviscoelasticity is discussed. Other specific topics include the topological properties of finite element models, applications to linear and nonlinear boundary value problems, convergence, continuum thermodynamics, finite elasticity, solutions to nonlinear partial differential equations, and discrete models of the nonlinear thermomechanical behavior of dissipative media.

Oden, J. T.↗
NASA NTRS1972

Two-dimensional finite-element temperature variance analysis

The finite element method is extended to thermal analysis by forming a variance analysis of temperature results so that the sensitivity of predicted temperatures to uncertainties in input variables is determined. The temperature fields within a finite number of elements are described in terms of the temperatures of vertices and the variational principle is used to minimize the integral equation describing thermal potential energy. A computer calculation yields the desired solution matrix of predicted temperatures and provides information about initial thermal parameters and their associated errors. Sample calculations show that all predicted temperatures are most effected by temperature values along fixed boundaries; more accurate specifications of these temperatures reduce errors in thermal calculations.

Heuser, J. S.↗
NASA NTRS1992

Finite element method for optimal guidance of an advanced launch vehicle

A temporal finite element based on a mixed form of Hamilton's weak principle is summarized for optimal control problems. The resulting weak Hamiltonian finite element method is extended to allow for discontinuities in the states and/or discontinuities in the system equations. An extension of the formulation to allow for control inequality constraints is also presented. The formulation does not require element quadrature, and it produces a sparse system of nonlinear algebraic equations. To evaluate its feasibility for real-time guidance applications, this approach is applied to the trajectory optimization of a four-state, two-stage model with inequality constraints for an advanced launch vehicle. Numerical results for this model are presented and compared to results from a multiple-shooting code. The results show the accuracy and computational efficiency of the finite element method.

Hodges, Dewey H.↗
NASA NTRS1988

A finite element method for time varying geometry in multibody structures

A three-dimensional finite element formulation using convected coordinates is presented for the multibody dynamics of truss-like configurations. Unlike existing formulations, the present one does not superimpose nonlinear rigid body kinematics with linear structural mode shapes, an approach that has recently been shown to be grossly inaccurate under certain conditions. Instead, the finite element method is extended to treat large motions/deformations. The formulation is oriented toward joint dominated structures and places the generalized coordinates at the joints. For the planar spin-up of a flexible beam, results are compared with those derived from a commercially available computer program. The two programs predict nearly identical results.

Housner, J. M.↗
NASA NTRS1989

A least-squares finite element method for incompressible Navier-Stokes problem

Most finite element schemes for solving the Navier-Stokes equations can be categorized into the Galerkin mixed method and the penalty method. The mixed method leads to a saddle-point problem. In order to guarantee the existence of a solution, the combination of velocity and pressure interpolations requires satisfaction of the Ladyzhenskaya Babuska Brezzi (LBB) consistency condition which precludes the use of equal order interpolations and many seemingly natural pairs of velocity and pressure elements. In a previous paper a least-squares finite element method based on the first order velocity-pressure-vorticity formulation for the Stokes problem was proposed. This method leads to a minimization problem. The choice of combination of elements is thus not subject to the LBB condition. The numerical experiments exhibit the optimal rate of convergence for all variables with equal order interpolations. A theoretical error analysis supports the numerical results. In this paper the least-squares finite element method is extended to solving the incompressible Navier-Stokes problem.

Jiang, Bonan↗
NASA NTRS1994

Radiation and scattering from cylindrically conformal printed antennas

Microstrip patch antennas offer considerable advantages in terms of weight, aerodynamic drag, cost, flexibility, and observables over more conventional protruding antennas. These flat patch antennas were first proposed over thirty years ago by Deschamps in the United States and Gutton and Baisinot in France. Such antennas have been analyzed and developed for planar as well as curved platforms. However, the methods used in these designs employ gross approximations, suffer from extreme computational burden, or require expensive physical experiments. The goal of this thesis is to develop accurate and efficient numerical modeling techniques which represent actual antenna structures mounted on curved surfaces with a high degree of fidelity. In this thesis, the finite element method is extended to cavity-backed conformal antenna arrays embedded in a circular, metallic, infinite cylinder. Both the boundary integral and absorbing boundary mesh closure conditions will be used for terminating the mesh. These two approaches will be contrasted and used to study the scattering and radiation behavior of several useful antenna configurations. An important feature of this study will be to examine the effect of curvature and cavity size on the scattering and radiation properties of wraparound conformal antenna arrays.

Kempel, Leo C.↗
NASA NTRSDate not supplied

Extending an Economical Third-Order Inviscid Nodal-Gradient Cell-Centered Finite-Volume Method to Mixed-Element Grids

In this paper, we extend an economical third-order nodal-gradient cell-centered finite-volume method, originally developed for tetrahedral grids, to mixed-element grids. It is shown that the efficient quadratic interpolation formula essential to eliminating second derivatives from a third-order accurate discretization can be easily extended to an arbitrary cell type. For the surface flux integration, we consider a split-face approach, where a quadrilateral face is split into two triangles, and the third-order method for tetrahedra is directly applied. Also, we derive a second-derivative-free, high-order, volume quadrature formula for an arbitrary cell. Numerical results are presented for accuracy verification and applications with three-dimensional nontetrahedral grids.

Computational Fluid Dynamics↗
NASA NTRS1999

High Order Approximations for Compressible Fluid Dynamics on Unstructured and Cartesian Meshes

The development of high-order accurate numerical discretization techniques for irregular domains and meshes is often cited as one of the remaining challenges facing the field of computational fluid dynamics. In structural mechanics, the advantages of high-order finite element approximation are widely recognized. This is especially true when high-order element approximation is combined with element refinement (h-p refinement). In computational fluid dynamics, high-order discretization methods are infrequently used in the computation of compressible fluid flow. The hyperbolic nature of the governing equations and the presence of solution discontinuities makes high-order accuracy difficult to achieve. Consequently, second-order accurate methods are still predominately used in industrial applications even though evidence suggests that high-order methods may offer a way to significantly improve the resolution and accuracy for these calculations. To address this important topic, a special course was jointly organized by the Applied Vehicle Technology Panel of NATO's Research and Technology Organization (RTO), the von Karman Institute for Fluid Dynamics, and the Numerical Aerospace Simulation Division at the NASA Ames Research Center. The NATO RTO sponsored course entitled "Higher Order Discretization Methods in Computational Fluid Dynamics" was held September 14-18, 1998 at the von Karman Institute for Fluid Dynamics in Belgium and September 21-25, 1998 at the NASA Ames Research Center in the United States. During this special course, lecturers from Europe and the United States gave a series of comprehensive lectures on advanced topics related to the high-order numerical discretization of partial differential equations with primary emphasis given to computational fluid dynamics (CFD). Additional consideration was given to topics in computational physics such as the high-order discretization of the Hamilton-Jacobi, Helmholtz, and elasticity equations. This volume consists of five articles prepared by the special course lecturers. These articles should be of particular relevance to those readers with an interest in numerical discretization techniques which generalize to very high-order accuracy. The articles of Professors Abgrall and Shu consider the mathematical formulation of high-order accurate finite volume schemes utilizing essentially non-oscillatory (ENO) and weighted essentially non-oscillatory (WENO) reconstruction together with upwind flux evaluation. These formulations are particularly effective in computing numerical solutions of conservation laws containing solution discontinuities. Careful attention is given by the authors to implementational issues and techniques for improving the overall efficiency of these methods. The article of Professor Cockburn discusses the discontinuous Galerkin finite element method. This method naturally extends to high-order accuracy and has an interpretation as a finite volume method. Cockburn addresses two important issues associated with the discontinuous Galerkin method: controlling spurious extrema near solution discontinuities via "limiting" and the extension to second order advective-diffusive equations (joint work with Shu). The articles of Dr. Henderson and Professor Schwab consider the mathematical formulation and implementation of the h-p finite element methods using hierarchical basis functions and adaptive mesh refinement. These methods are particularly useful in computing high-order accurate solutions containing perturbative layers and corner singularities. Additional flexibility is obtained using a mortar FEM technique whereby nonconforming elements are interfaced together. Numerous examples are given by Henderson applying the h-p FEM method to the simulation of turbulence and turbulence transition.

Barth, Timothy↗
NASA NTRS2009

Multiscale Failure Analysis of Laminated Composite Panels Subjected to Blast Loading Using FEAMAC/Explicit

This preliminary report demonstrates the capabilities of the recently developed software implementation that links the Generalized Method of Cells to explicit finite element analysis by extending a previous development which tied the generalized method of cells to implicit finite elements. The multiscale framework, which uses explicit finite elements at the global-scale and the generalized method of cells at the microscale is detailed. This implementation is suitable for both dynamic mechanics problems and static problems exhibiting drastic and sudden changes in material properties, which often encounter convergence issues with commercial implicit solvers. Progressive failure analysis of stiffened and un-stiffened fiber-reinforced laminates subjected to normal blast pressure loads was performed and is used to demonstrate the capabilities of this framework. The focus of this report is to document the development of the software implementation; thus, no comparison between the results of the models and experimental data is drawn. However, the validity of the results are assessed qualitatively through the observation of failure paths, stress contours, and the distribution of system energies.

Pineda, Evan J.↗
NASA NTRS1984

A finite element method for nonlinear forced vibrations of rectangular plates

The finite element method has been extended to determine the response of large amplitude forced vibrations of thin plates. A harmonic force matrix of a rectangular element under uniform harmonic excitation is developed for nonlinear forced vibration analysis. Inplane deformation and inertia are both considered in the formulation. Results obtained are compared with simple elliptic response, perturbation and other approximation solutions.

Mei, C.↗
NASA NTRS1994

Finite element method for eigenvalue problems in electromagnetics

Finite element method (FEM) has been a very powerful tool to solve many complex problems in electromagnetics. The goal of the current research at the Langley Research Center is to develop a combined FEM/method of moments approach to three-dimensional scattering/radiation problem for objects with arbitrary shape and filled with complex materials. As a first step toward that goal, an exercise is taken to establish the power of FEM, through closed boundary problems. This paper demonstrates the developed of FEM tools for two- and three-dimensional eigenvalue problems in electromagnetics. In section 2, both the scalar and vector finite elements have been used for various waveguide problems to demonstrate the flexibility of FEM. In section 3, vector finite element method has been extended to three-dimensional eigenvalue problems.

Reddy, C. J.↗
NASA NTRS2002

Calculation of Scattering Amplitude Without Partial Analysis: Inclusion of Exchange - II

There was a method for calculating the whole scattering amplitude, f(Omega(sub k)), directly. The idea was to calculate the complete wave function Psi numerically, and use it in an integral expression for f, which can be reduced to a 2 dimensional quadrature. The original application was for e-H scattering without exchange. There the Schrodinger reduces a 2-d partial differential equation (pde), which was solved using the finite element method (FEM). Here we extend the method to the exchange approximation. The S.E. can be reduced to a pair of coupled pde's, which are again solved by the FEM. The formal expression for f(Omega(sub k)) consists two integrals, f+/- = f(sub d) +/- f(sub e); f(sub d) is formally the same integral as the no-exchange f. We have also succeeded in reducing f(sub e) to a 2-d integral. Results will be presented at the meeting.

Temkin, Aaron↗
NASA NTRS1981

Scattering of Pruppacher-Pitter raindrops at 30 GHz

Optimum design of modern ground-satellite communication systems requires the knowledge of rain-induced differential attenuation, differential phase shift, and cross polarization factors. Different available analytical techniques for raindrop scattering problems were assessed. These include: (1) geometrical theory of diffraction; (2) method of moment; (3) perturbation method; (4) point matching methods; (5) extended boundary condition method; and (6) global-local finite element method. The advantages and disadvantages of each are listed. The extended boundary condition method, which was determined to yield the most scattering results, is summarized. The scattered fields for Pruppacher-Pitter raindrops with sizes ranging from 0.5 mm to 3.5 mm at 20 C and at 30 GHz for several incidence angles are tabulated.

Yeh, C.↗
NASA NTRS2008

Damage Diagnosis in Semiconductive Materials Using Electrical Impedance Measurements

Recent aerospace industry trends have resulted in an increased demand for real-time, effective techniques for in-flight structural health monitoring. A promising technique for damage diagnosis uses electrical impedance measurements of semiconductive materials. By applying a small electrical current into a material specimen and measuring the corresponding voltages at various locations on the specimen, changes in the electrical characteristics due to the presence of damage can be assessed. An artificial neural network uses these changes in electrical properties to provide an inverse solution that estimates the location and magnitude of the damage. The advantage of the electrical impedance method over other damage diagnosis techniques is that it uses the material as the sensor. Simple voltage measurements can be used instead of discrete sensors, resulting in a reduction in weight and system complexity. This research effort extends previous work by employing finite element method models to improve accuracy of complex models with anisotropic conductivities and by enhancing the computational efficiency of the inverse techniques. The paper demonstrates a proof of concept of a damage diagnosis approach using electrical impedance methods and a neural network as an effective tool for in-flight diagnosis of structural damage to aircraft components.

Ross, Richard W.↗