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NASA NTRS1992

Reduced basis technique for calculating sensitivity coefficients of nonlinear structural response

An efficient reduced basis technique is presented for calculating the sensitivity of nonlinear structural response to variations in the design variables. The structure is discretized by using two-field mixed finite element models. The vector of structural response and its sensitivity coefficients (derivatives with respect to design variables) are each expressed as a linear combination of a small number of basis (or global approximation) vectors. The Bubnov-Galerkin technique is then used to approximate each of the finite element equations governing the response and the sensitivity coefficients by a small number of algebraic equations in the amplitudes of these vectors. The path derivatives (derivatives of the response vector with respect to path parameters, e.g., load parameters) are used as basis vectors for approximating the response. A combination of the path derivatives and their derivatives with respect to the design variables is used for approximating the sensitivity coefficients. The potential of the proposed technique is discussed and its effectiveness is demonstrated by means of numerical examples of laminated composite plates subjected to mechanical and thermal loads.

Noor, Ahmed K.↗

NASA NTRS1994

Transverse shear stresses and their sensitivity coefficients in multilayered composite panels

A computational procedure is presented for the accurate determination of transverse shear stresses and their sensitivity coefficients in flat multilayered composite panels subjected to mechanical and thermal loads. The sensitivity coefficients measure the sensitivity of the transverse shear stresses to variations in the different lamination and material parameters of the panel. The panel is discretized by using either a three-field mixed finite element model based on a two-dimensional first- order shear deformation plate theory or a two-field degenerate solid element with each of the displacement components having a linear variation throughout the thickness of the laminate. The evaluation of transverse shear stresses can be conveniently divided into two phases. The first phase consists of using a superconvergent recovery technique for evaluating the in-plane stresses in the different layers. In the second phase, the transverse shear stresses are evaluated by using piecewise integration, in the thickness direction, of the three-dimensional equilibrium equations. The same procedure is used for evaluating the sensitivity coefficients of the transverse shear stresses. The effectiveness of the computational procedure is demonstrated by means of numerical examples of multilayered cross-ply panels subjected to transverse loading, uniform temperature change, and uniform temperature gradient through the thickness of the panel. In each case the standard of the comparison is taken to be the exact solution of the three dimensional thermoelasticity equations of the panel.

Noor, Ahmed K.↗

NASA NTRS1996

First-Order System Least-Squares for Second-Order Elliptic Problems with Discontinuous Coefficients

The first-order system least-squares methodology represents an alternative to standard mixed finite element methods. Among its advantages is the fact that the finite element spaces approximating the pressure and flux variables are not restricted by the inf-sup condition and that the least-squares functional itself serves as an appropriate error measure. This paper studies the first-order system least-squares approach for scalar second-order elliptic boundary value problems with discontinuous coefficients. Ellipticity of an appropriately scaled least-squares bilinear form of the size of the jumps in the coefficients leading to adequate finite element approximation results. The occurrence of singularities at interface corners and cross-points is discussed. and a weighted least-squares functional is introduced to handle such cases. Numerical experiments are presented for two test problems to illustrate the performance of this approach.

Manteuffel, Thomas A.↗

NASA NTRS1995

Simulation of thin slot spirals and dual circular patch antennas using the finite element method with mixed elements

This semi-annual report describes progress up to mid-January 1995. The report contains five sections all dealing with the modeling of spiral and patch antennas recessed in metallic platforms. Of significance is the development of decomposition schemes which separate the different regions of the antenna volume. Substantial effort was devoted to improving the feed model in the context of the finite element method (FEM). Finally, an innovative scheme for truncating finite element meshes is presented.

Gong, Jian↗

NASA NTRS1986

Stability and natural vibration analysis of laminated plates by using a mixed element based on a refined plate theory

A mixed shear flexible finite element, with relaxed continuity, is developed for the geometrically linear and nonlinear analysis of layered anisotropic plates. The element formulation is based on a refined higher order theory which satisfies the zero transverse shear stress boundary conditions on the top and bottom faces of the plate and requires no shear correction coefficients. The mixed finite element developed herein consists of eleven degrees of freedom per node which include three displacements, two rotations and six moment resultants. The element is evaluated for its accuracy in the analysis of the stability and vibration of anisotropic rectangular plates with different lamination schemes and boundary conditions. The mixed finite element described here for the higher order theory gives very accurate results for buckling loads and natural frequencies.

Putcha, N. S.↗

NASA NTRS1986

Composite interlaminar fracture toughness: Three-dimensional finite element modeling for mixed mode 1, 2 and 3 fracture

A computational method/procedure is described which can be used to simulate individual and mixed mode interlaminar fracture progression in fiber composite laminates. Different combinations of Modes 1, 2, and 3 fracture are simulated by varying the crack location through the specimen thickness and by selecting appropriate unsymmetric laminate configurations. The contribution of each fracture mode to strain energy release rate is determined by the local crack closure methods while the mixed mode is determined by global variables. The strain energy release rates are plotted versus extending crack length, where slow crack growth, stable crack growth, and rapid crack growth regions are easily identified. Graphical results are presented to illustrate the effectiveness and versatility of the computational simulation for: (1) evaluating mixed-mode interlaminar fracture, (2) for identifying respective dominant parameters, and (3) for selecting possible simple test methods.

Murthy, P. L. N.↗

NASA NTRS1988

Composite interlaminar fracture toughness - Three-dimensional finite-element modeling for mixed mode I, II, and fracture

Murthy, Pappu L. N.↗

NASA NTRS1988

An approach to probabilistic finite element analysis using a mixed-iterative formulation

An efficient algorithm for computing the response sensitivity of finite element problems based on a mixed-iterative formulation is proposed. This method does not involve explicit differentiation of the tangent stiffness array and can be used with formulations for which a consistent tangent stiffness is not readily available. The method has been successfully applied to probabilistic finite element analysis of problems using the proposed mixed formulation, and this exercise has provided valuable insights regarding the extension of the method to a more general class of problems to include material and geometric nonlinearities.

Dias, J. B.↗

NASA NTRS1996

FEM R-Matrix Calculations of Electron-H2 Collisions

Electron-H2 Collisions have been studied using the finite-element R-matrix method. Our approach uses a mixed finite-element and Gaussian basis to describe the continuum electron. In the inner region, the multi-centered nature of the Gaussian basis provides an efficient representation in the regions of space near the nuclei, whereas the piecemeal and energy-independent nature of the FEM basis is particular well suited for R-matrix calculations. Fixed nuclei calculations have been carried out at 1.4 a(sub 0), the equilibrium internuclear distance of the ground state. Up to six target states are included: the X(sup 1)E+(sub g), b(sup 3)E+(sub u), a(sup 3)E+(sub g), B(sup 1)E+(sub u), c(sup 3)II(sub u), and C(sup 1)II(sub u) states, and configuration-interaction functions are used to describe the target states. The results will be compared with available theoretical and experimental data.

Huo, Winifred M.↗

NASA NTRS1999

A Mixed Multi-Field Finite Element Formulation for Thermopiezoelectric Composite Shells

Analytical formulations are presented which account for the coupled mechanical, electrical, and thermal response of piezoelectric composite shell structures. A new mixed multi-field laminate theory is developed which combines "single layer" assumptions for the displacements along with layerwise fields for the electric potential and temperature. This laminate theory is formulated using curvilinear coordinates and is based on the principles of linear thermopiezoelectricity. The mechanics have the inherent capability to explicitly model both the active and sensory responses of piezoelectric composite shells in thermal environment. Finite element equations are derived and implemented for an eight-noded shell element. Numerical studies are conducted to investigate both the sensory and active responses of piezoelectric composite shell structures subjected to thermal loads. Results for a cantilevered plate with an attached piezoelectric layer are com- pared with corresponding results from a commercial finite element code and a previously developed program. Additional studies are conducted on a cylindrical shell with an attached piezoelectric layer to demonstrate capabilities to achieve thermal shape control on curved piezoelectric structures.

Lee, Ho-Jun↗

NASA NTRS1990

Mixed variational formulation of finite element analysis of acoustoelastic/slosh fluid-structure interaction

A general three-field variational principle is obtained for the motion of an acoustic fluid enclosed in a rigid or flexible container by the method of canonical decomposition applied to a modified form of the wave equation in the displacement potential. The general principle is specialized to a mixed two-field principle that contains the fluid displacement potential and pressure as independent fields. This principle contains a free parameter alpha. Semidiscrete finite-element equations of motion based on this principle are displayed and applied to the transient response and free-vibrations of the coupled fluid-structure problem. It is shown that a particular setting of alpha yields a rich set of formulations that can be customized to fit physical and computational requirements. The variational principle is then extended to handle slosh motions in a uniform gravity field, and used to derived semidiscrete equations of motion that account for such effects.

Felippa, C. A.↗

NASA NTRS1991

Mixed variational formulations of finite element analysis of elastoacoustic/slosh fluid-structure interaction

A general three-field variational principle is obtained for the motion of an acoustic fluid enclosed in a rigid or flexible container by the method of canonical decomposition applied to a modified form of the wave equation in the displacement potential. The general principle is specialized to a mixed two-field principle that contains the fluid displacement potential and pressure as independent fields. This principle contains a free parameter alpha. Semidiscrete finite-element equations of motion based on this principle are displayed and applied to the transient response and free-vibrations of the coupled fluid-structure problem. It is shown that a particular setting of alpha yields a rich set of formulations that can be customized to fit physical and computational requirements. The variational principle is then extended to handle slosh motions in a uniform gravity field, and used to derive semidiscrete equations of motion that account for such effects.

Felippa, Carlos A.↗

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 NTRS1984

Mixed Models and Reduction Techniques for Large-Rotation, Nonlinear Analysis of Shells of Revolution with Application to Tires

An effective computational strategy is presented for the large-rotation, nonlinear axisymmetric analysis of shells of revolution. The three key elements of the computational strategy are: (1) use of mixed finite-element models with discontinuous stress resultants at the element interfaces; (2) substantial reduction in the total number of degrees of freedom through the use of a multiple-parameter reduction technique; and (3) reduction in the size of the analysis model through the decomposition of asymmetric loads into symmetric and antisymmetric components coupled with the use of the multiple-parameter reduction technique. The potential of the proposed computational strategy is discussed. Numerical results are presented to demonstrate the high accuracy of the mixed models developed and to show the potential of using the proposed computational strategy for the analysis of tires.

Noor, A. K.↗

NASA NTRS1996

Coupled mixed-field laminate theory and finite element for smart piezoelectric composite shell structures

Mechanics for the analysis of laminated composite shells with piezoelectric actuators and sensors are presented. A new mixed-field laminate theory for piezoelectric shells is formulated in curvilinear coordinates which combines single-layer assumptions for the displacements and a layerwise representation for the electric potential. The resultant coupled governing equations for curvilinear piezoelectric laminates are described. Structural mechanics are subsequently developed and an 8-node finite-element is formulated for the static and dynamic analysis of adaptive composite structures of general laminations containing piezoelectric layers. Evaluations of the method and comparisons with reported results are presented for laminated piezoelectric-composite plates, a closed cylindrical shell with a continuous piezoceramic layer and a laminated composite semi-circular cantilever shell with discrete cylindrical piezoelectric actuators and/or sensors.

Saravanos, Dimitris A.↗

NASA NTRS1987

Exploiting symmetries in the modeling and analysis of tires

A simple and efficient computational strategy for reducing both the size of a tire model and the cost of the analysis of tires in the presence of symmetry-breaking conditions (unsymmetry in the tire material, geometry, or loading) is presented. The strategy is based on approximating the unsymmetric response of the tire with a linear combination of symmetric and antisymmetric global approximation vectors (or modes). Details are presented for the three main elements of the computational strategy, which include: use of special three-field mixed finite-element models, use of operator splitting, and substantial reduction in the number of degrees of freedom. The proposed computational stategy is applied to three quasi-symmetric problems of tires: linear analysis of anisotropic tires, through use of semianalytic finite elements, nonlinear analysis of anisotropic tires through use of two-dimensional shell finite elements, and nonlinear analysis of orthotropic tires subjected to unsymmetric loading. Three basic types of symmetry (and their combinations) exhibited by the tire response are identified.

Noor, Ahmed K.↗

NASA NTRS1990

Free vibrations of thin-walled semicircular graphite-epoxy composite frames

A detailed study is made of the effects of variations in lamination and material parameters of thin walled composite frames on their vibrational characteristics. The structures considered are semicircular thin walled frames with I and J sections. The flanges and webs of the frames are modeled by using 2-D shell and plate finite elements. A mixed formulation is used with the fundamental unknowns consisting of both the generalized displacements and stress resultants in the frame. The frequencies and modes predicted by the 2-D finite element model are compared with those obtained from experiments, as well as with the predictions of a non-dimensional thin walled beam finite element model. A detailed study is made of the sensitivity of the vibrational response to variations in the fiber orientation, material properties of the individual layers, and boundary conditions.

Carden, Huey D.↗

NASA NTRS1990

Free vibrations of thin-walled semicircular graphite-epoxy composite frames

A detailed study is made of the effects of variations in lamination and material parameters of thin walled composite frames on their vibrational characteristics. The structures considered are semicircular thin walled frames with I and J sections. The flanges and webs of the frames are modelled by using 2-D shell and plate finite elements. A mixed formulation is used with the fundamental unknowns consisting of both the generalized displacements and stress resultants in the frames. The frequencies and modes predicted by the 2-D finite element model are compared with those obtained from experiments, as well as with the predictions of a 1-D thin walled beam finite element model. A detailed study is made of the sensitivity of the vibrational response to variations in the fiber orientation, material properties of the individual layers, and boundary conditions.

Noor, Ahmed K.↗