Schenk C.A., Schueller G.I. — Uncertainty Assessment of Large Finite Element Systems :: Электронная библиотека попечительского совета мехмата МГУ

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Schenk C.A., Schueller G.I. — Uncertainty Assessment of Large Finite Element Systems

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Название: Uncertainty Assessment of Large Finite Element Systems

Авторы: Schenk C.A., Schueller G.I.

Аннотация:

The treatment of uncertainties in the analysis of engineering structures remains one of the premium challenges in structural mechanics. It is only in recent years that the developments in stochastic and deterministic computational mechanics began to be synchronized. In this monograph novel computational procedures for the uncertainty assessment of large finite element systems are presented. The procedures are applicable to well known problems in computational stochastic mechanics, such as the stability analysis of systems with random imperfections and the dynamic analysis of deterministic systems under stochastic loading. For the dynamic analysis of deterministic systems under stochastic loading, an efficient procedure based on the Karhunen-Loeve representation of the response is presented. The capabilities of the developed procedures are demonstrated with several numerical examples.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2005

Количество страниц: 160

Добавлена в каталог: 14.05.2008

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Предметный указатель

Algebraic eigenvalue problem      47 110
Arc-length control technique      23 25
Asymptotic analysis      21
Bi-cubic interpolation      95
Bifurcation points      21
Bouc — Wen model      5 68
Boundary imperfections      82 87 98
Boundedness      12
Buckling      21
Cauchy sequence      12
Centered processes      148
Central limit theorem      40
Central moments      41
Cholesky decomposition      14
Collapse      21
colon      47
Colored noise      149
Completeness      12
Complex modal analysis      5
Continuation methods      21
Continuous Karhunen — Loeve expansion      47 53
Correlation coefficient function      81
correlation length      81
Covariance function      41 45
Covariance matrix      6 40 47 69 110 148
Critical load      3 25
Critical points      21
Cumulative distribution function      41
Cutout      4 94
Differential equilibrium      18
Dirac's delta function      149
Direct integration      28
Discrete Karhunen — Loeve expansion      47
Discretization      46
Displacement interpolation matrix      18
Displacement-based finite element method      17
Distribution matrix      110
Donnell type equations      89
Duhamel integral method      31
Earthquake excitation      5 65 125
Effective stiffness matrix      29
Eigenvalue, decomposition      14
Eigenvalue, matrix      14
Element equilibrium      18
Equivalent statistical linearization      65
Ergodicity      83
Estimated covariance matrix      80
Evolutionary spectra      111
Expansion theorem      13
Expectation operator      40
Fast Fourier Transform      42
Filter      109
Filtered white noise      4 109
Finite dimensional domains      12
Finite dimensional vector spaces      12
Flexibility matrix      32
Fokker — Planck equations      5
Follower forces      22
Fourier series      4 85
Fourier series theorem      46
Fredholm integral equation      53
Frequency response function      111
Frequency response functions      5
Fundamental matrix      147
Fundamental path      24
Gaussian stochastic process      39 40 46
General non-linear analysis      21
Generalized eigenvalue problem      14 25
Geometric imperfections      3 79 83
Global coordinates      18
Ground accelerations      110
Gyroscopic and circulatory forces      30
Heaviside step function      118
Hilbert spaces      12 46
histogram      96
Homogeneous random field      81
Hourglass modes      84
Hysteresis loop      68 70
Idempotent      13
Identity matrix      147
Imperfection database      141
Implicit integration      29
Inter-story stiffness      124
Interpolation method      52
Isotropic cylindrical shell      79
Jacobian matrix      22
Joint probability density function      40
Karhunen — Loeve expansion      11 46
Karhunen — Loeve representation      5 110
Karhunen — Loeve vector      65 74
Karhunen — Loeve vectors      47

Knock down factors      3
Koiter's method      21
Kronecker delta      15
Lagrange multiplier      84
Limit points      21
Linearization coefficients      62 70
Linearized buckling analysis      14
Local averaging method      52
Lyapunov matrix differential equation      5 110 127 148
Markov process      5
Mean function      41 45
Mean vector      40
Mean-square error      46
Modal coordinates      31 32
Modal damping      31 127
Modal geometric imperfections      104
Modal Lyapunov matrix differential equation      121
Modal matrix      14
Mode, acceleration method      31 32
Mode, displacement method      31
Mode, truncation      28
Monte Carlo simulation      58 79 94 96
Natural strain element      83
Newmark integration      28
Newton — Raphson, full      23
Newton — Raphson, modified      23 95
Nodal point equilibrium      18
Non-defective      14
Non-Gaussian models      40
Non-homogeneous random field      80
Non-zero mean response      74
Nystroem method      53
Operator      11
Orthogonal projections      13
orthogonal series      12
Orthogonal series representation      45
Orthonormal functions      45
Orthonormality relation      47
Perturbation theory      21
Plastic elongations      117
Point discretization methods      52
Polynomial chaos expanions      43
Power spectral density      110 149
Pre-buckling      88 96
Principal component analysis      47
Principal matrix      147
Principal of virtual work      17
Probability density function      38 41
Proportional damping      31 122
Random coefficients      46
Random trigonometric polynomials      46
Random variables      38
Randomness      1
Reliability analysis      112
Resolution of the identity      13
Runge — Kutta      112
Safety factors      1
Second order stochastic processes      45
Secondary solution paths      25
Self adjoint matrix operator      112
Separable correlation structure      81
Single degree of freedom system      113
Snap-through      21 25 95
Spectral matrix      148
Spectral representation      42
Spectral theorem      12 13 51
Standard eigenvalue problem      14 25
Standard normal space      97
State space      113 147
Stationarity      41
Stationary process      39
Stochastic processes      11 40
Strain-displacement matrix      18
Superposition principle      65 69
System matrix      122 147
Tangent stiffness matrix      22 25
Taylor series      22
Thickness imperfections      3
Time invariant systems      147
Time modulation function      111
Transformation with memory      61
Trapezoidal integration      72
Tschebyschev's inequality      59
Uncertainties      1 37
Uncertainty      38 40 86
Unconditionally stable integration      28
Wavelet — Galerkin scheme      53
White noise      115 148
White noise intensity      149
Zero mean Gaussian stochastic processes      46
Zero mean loading process      70

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