## A numerically efficient finite element hydroelastic analysis: volume 1--theory and results |

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1/8-Scale External Tank 1/8-Scale Space Shuttle analysis set axial Circular Cylindrical Shell circumferential harmonics classical mechanics complementary virtual computational consists constraints coordinates degrees of freedom derivation discrete dynamic equation set Euler-Lagrange equations fill conditions Filled Circular Cylindrical finite element hydroelastic Finite Element Model flexibility matrix fluid and structural Fluid Filled Circular fluid mass matrix free surface Frequency Spectra g-set grid set Guyan reduction Hamilton's principle harmonic reduction Hemispherical Container hydroelastic equations hydroelastic formulation illustrated in Fig impulse incompressible fluid incompressible fluid flow inertance matrix inverse inviscid kinetic and strain modal mode shapes NASA NASTRAN hydroelastic analysis natural frequencies Post Max Q pressure deviation radial recovery relationship reference frame Fig Rigid Format 13 Shuttle External Tank Space Shuttle External Spherical Cap spherical reference frame static pressurization stiffness matrix strain energies structural grid surface displacements thermal Toupin's principle uniform pressure unpressurized Unsymmetric Cylinder