A NASTRAN implementation of the doubly asymptotic approximation for underwater shock response

A detailed description is given of how the decoupling approximation known as the doubly asymptotic approximation is implemented with NASTRAN to solve shock problems for submerged structures. The general approach involves locating the nonsymmetric terms (which couple structural and fluid variables) on the right hand side of the equations. This approach results in coefficient matrices of acceptable bandwidth but degrades numerical stability, requiring a smaller time step size than would otherwise be used. It is also shown how the structure's added (virtual) mass matrix, is calculated with NASTRAN

Recent improvements to BANDIT

The NASTRAN preprocessor BANDIT, which improves NASTRAN's computer efficiency by resequencing grid point labels for reduced matrix bandwidth is described. The addition of (1) the Gibbs-Poole-Stockmeyer (GPS) algorithm, and (2) the user option to reduce matrix profile rather than matrix bandwidth is also described. It is shown that, compared to the Cuthill-McKee algorithm on which BANDIT was originally based, GPS is faster and achieves similar results. Current capabilities and options of BANDIT are summarized

Calculation of low frequency vibrational resonances of submerged structures

Numerical techniques for calculating the low frequency vibrational resonances of submerged structures are reviewed. Both finite element and boundary element approaches for calculating fully-coupled added mass matrices for use in NASTRAN analysis are described and illustrated. The finite element approach is implemented using existing capability in NASTRAN. The boundary element approach uses the NASHUA structural-acoustics program to compute the added mass matrix. The two procedures are compared to each other for the case of a submerged cylindrical shell with flat end closures. It is concluded that both procedures are capable of computing accurate submerged resonances and that the more elegant boundary element procedure is easier to use but may be more expensive computationally

Reduction of matrix wavefront for NASTRAN

The three grid point resequencing algorithms most often run by NASTRAN users are compared for their ability to reduce matrix root-mean-square (rms) wavefront, which is the most critical parameter in determining matrix decomposition time in NASTRAN. The three algorithms are Cuthill-McKee (CM), Gibbs-Poole-Stockmeyer (GPS), and Levy. The first two (CM and GPS) are in the BANDIT program, and the Levy algorithm is in WAVEFRONT. Results are presented for a diversified collection of 30 test problems ranging in size from 59 to 2680 nodes. It is concluded that GPS is exceptionally fast and, for the conditions under which the test was made, the algorithm best able to reduce rms wavefront consistently well

Acoustic intensity calculations for axisymmetrically modeled fluid regions

An algorithm for calculating acoustic intensities from a time harmonic pressure field in an axisymmetric fluid region is presented. Acoustic pressures are computed in a mesh of NASTRAN triangular finite elements of revolution (TRIAAX) using an analogy between the scalar wave equation and elasticity equations. Acoustic intensities are then calculated from pressures and pressure derivatives taken over the mesh of TRIAAX elements. Intensities are displayed as vectors indicating the directions and magnitudes of energy flow at all mesh points in the acoustic field. A prolate spheroidal shell is modeled with axisymmetric shell elements (CONEAX) and submerged in a fluid region of TRIAAX elements. The model is analyzed to illustrate the acoustic intensity method and the usefulness of energy flow paths in the understanding of the response of fluid-structure interaction problems. The structural-acoustic analogy used is summarized for completeness. This study uncovered a NASTRAN limitation involving numerical precision issues in the CONEAX stiffness calculation causing large errors in the system matrices for nearly cylindrical cones

Comparison of finite element analysis of a piping tee using NASTRAN and CORTES/SA

A comparison of finite element analyses of a piping tee was made using NASTRAN and CORTES/SA, a modified version of SAP3 having a special purpose input processor for generating geometries for a wide variety of tee joints. Four finite element models were subjected in force, moment, and pressure loadings. Flexibility factors and principal stresses were computed for each model and compared with results obtained experimentally by Combustion Engineering, Inc. Results from the NASTRAN analyses were in good agreement with experimental results for all loadings except internal pressure. The CORTES/SA analyses gave good results for the internal pressure loading, but poorer results for out of plane bending moments or forces resulting in out of plane bending. Two of the basic load cases in CORTES/SA were found to contain errors that could not be easily corrected. COST COMPARison of NASTRAN and CORTES/SA showed NASTRAN to be less expensive to two than CORTES/SA for identical meshes

Coupled BE/FE/BE approach for scattering from fluid-filled structures

NASHUA is a coupled finite element/boundary element capability built around NASTRAN for calculating the low frequency far-field acoustic pressure field radiated or scattered by an arbitrary, submerged, three-dimensional, elastic structure subjected to either internal time-harmonic mechanical loads or external time-harmonic incident loadings. Described here are the formulation and use of NASHUA for solving such structural acoustics problems when the structure is fluid-filled. NASTRAN is used to generate the structural finite element model and to perform most of the required matrix operations. Both fluid domains are modeled using the boundary element capability in NASHUA, whose matrix formulation (and the associated NASTRAN DMAP) for evacuated structures can be used with suitable interpretation of the matrix definitions. After computing surface pressures and normal velocities, far-field pressures are evaluated using an asymptotic form of the Helmholtz exterior integral equation. The proposed numerical approach is validated by comparing the acoustic field scattered from a submerged fluid-filled spherical thin shell to that obtained with a series solution, which is also derived here

The dynamic analysis of submerged structures

Methods are described by which the dynamic interaction of structures with surrounding fluids can be computed by using finite element techniques. In all cases, the fluid is assumed to behave as an acoustic medium and is initially stationary. Such problems are solved either by explicitly modeling the fluid (using pressure or displacement as the basic fluid unknown) or by using decoupling approximations which take account of the fluid effects without actually modeling the fluid

Finite element analysis of fluid-filled elastic piping systems

Two finite element procedures are described for predicting the dynamic response of general 3-D fluid-filled elastic piping systems. The first approach, a low frequency procedure, models each straight pipe or elbow as a sequence of beams. The contained fluid is modeled as a separate coincident sequence axial members (rods) which are tied to the pipe in the lateral direction. The model includes the pipe hoop strain correction to the fluid sound speed and the flexibility factor correction to the elbow flexibility. The second modeling approach, an intermediate frequency procedure, follows generally the original Zienkiewicz-Newton scheme for coupled fluid-structure problems except that the velocity potential is used as the fundamental fluid unknown to symmetrize the coefficient matrices. From comparisons of the beam model predictions to both experimental data and the 3-D model, the beam model is validated for frequencies up to about two-thirds of the lowest fluid-filled labor pipe mode. Accurate elbow flexibility factors are seen to be crucial for effective beam modeling of piping systems