Spectral Analysis of Deteriorated Offshore Structures

2007 ◽  
Author(s):  
H. Karadeniz
Keyword(s):  
Failure Mechanism ◽  
Stiffness Matrix ◽  
Progressive Failure ◽  
Offshore Structures ◽  
Mode Shapes ◽  
Solution Technique ◽  
Random Load ◽  
Practical Applications ◽  
Mass Matrices ◽  
Load Vector

In order to present an efficient, practical technique to determine progressive failure mechanism of structures, modelling of member deterioration by using a spring system is outlined. The procedure uses updates of member stiffness and mass matrices as well as the random load vector in incremental forms. In this procedure, the assembly process produces redistributions of the system stiffness and mass matrices, and the load vector. In the calculation of response spectral values, the original forms remain unchanged. Inversion of the stiffness matrix is calculated by using the Neumann expansion solution in which the original stiffness matrix is inverted only once so that a considerable computation time is saved in the whole calculation process. An incremental solution technique is presented for spectral analyses of both static and dynamic sensitive structures. In the case of dynamic analysis, special attention is paid to estimations of modified natural frequencies and mode shapes of deteriorated structures, which may affect response spectral values considerably. The technique, which is presented in the paper, is attractive in practical applications and can be efficiently used in the reliability calculation as well, and also it can be successfully used to determine a progressive failure mechanism of the structure.

Uncertainty Modelling and Fatigue Reliability Calculation of Offshore Structures With Deteriorated Members

2004 ◽  
Author(s):  
H. Karadeniz
Keyword(s):  
Probability Distribution ◽  
Stiffness Matrix ◽  
Transfer Functions ◽  
Offshore Structures ◽  
Solution Technique ◽  
Response Analysis ◽  
Reliability Calculation ◽  
Uncertainty Space ◽  
Uncertainty Parameter

This paper presents formulations and procedure of an efficient calculation of stress spectra and fatigue damage of offshore structures with deteriorated members in the uncertainty space. Calculation modeling of member deteriorations is represented by equivalent spring systems, which can be determined on basis of damage detection and stiffness degradation, with a deterioration uncertainty parameter. Redistributions of the member and system stiffness matrices and the load vectors are expressed in incremental (decremental) forms. The updated system stiffness-matrix is sated in terms of stiffness- and deterioration-uncertainties and the updated system load-vector is stated in terms of deterioration- and loading-uncertainties. Using the Neumann expansion solution technique, the inversion of the updated system stiffness matrix is expressed in terms of uncertainty parameters so that the reliability iteration can be performed without requiring repetitive inversion of the stiffness matrix. The deterioration- and uncertainty-update of the stiffness matrix requires resolution of the eigenvalue problem. This problem is reformulated in terms of uncertainty variables and an efficient solution algorithm is presented. An extra uncertainty parameter is used in structural transfer functions to represent damping uncertainties. Having expressed wave forces as functions of uncertainty variables, formulations of transfer functions of displacements and member internal forces are presented in the uncertainty space, which enable the reliability calculation to be efficient and fast. Apart from uncertainties of structural and loading origins, uncertainties arising from environmental origin, which appear in the spectral-analysis, are summarized. These are related to the modeling of random waves and wave-current interactions as well as to the long-term probability-distribution model of the significant wave height. Uncertainties in SCF, damage model (S-N line), non-narrowness of the stress process, long-term probability distribution of sea states and in the damage at which failure occurs (reference damage) are considered in fatigue-related uncertainties. An example is presented to demonstrate the application of the approximate analysis procedure to the mean value response analysis of deteriorated structures.

A Calculation Model for Deteriorated Members of 3D Frame Structures in the Static and Dynamic Analyses

2010 ◽  
Author(s):  
H. Karadeniz
Keyword(s):  
Structural Analysis ◽  
Degrees Of Freedom ◽  
Natural Frequencies ◽  
Calculation Model ◽  
Mode Shapes ◽  
Special Treatment ◽  
Structural System ◽  
Mass Matrices ◽  
Load Carrying ◽  
Load Vector

Jacket type structures in offshore structural industry consist of a large number of tubular members with various dimensions, which are joined to each other by welding that makes connections to be rigid. Diagonal members have relatively small dimensions, legs or chords have larger dimensions in general. Although the connections at joints are made rigidly, the actual joint behaviors under wave loadings are not fully rigid in the vicinity of connections due to local deformations of members having large diameters. In the short term, due to ultimate wave and earthquake loadings, some plastic deformations can also occur in members at some critical joints so that related members cannot be behave as rigidly connected and some releases of member forces occur. In the long term, fatigue damages can be observed at some joints that damaged members loose their functionality partly or fully as depending on damage rates. All these phenomena can be considered as member deterioration. A special treatment of deteriorated members can be used in the structural analysis by using a computation model that allows flexibility of damaged members at joints. The solution of this problem can be achieved by introducing a fictitious member concept, which can be derived as depending on actual member dimensions and joint configurations. The technique of using fictitious members introduces additional degrees of freedom that are not desirable in the analysis. A procedure which uses modified stiffness and mass matrices for flexibly connected members are more practical and attractive since a) no additional degrees of freedom are introduced, b) member-release and fixed-connection conditions can be directly obtained, c) a general member-end condition in any direction can be easily specified, d) a failure mechanism can be easily determined, e) in the fatigue damage calculation the load carrying capacity of the member can be used until the whole member cross-section is damaged and f) natural frequencies and mode shapes of damaged structural system can be estimated in terms of the natural frequencies and mode shapes of the undamaged structural system. The paper introduces a general formulation of a partly connected member to be used in structural analysis. For this purpose, a spring-beam element is defined using massless spring systems at member ends. An algorithmic procedure is presented to update member stiffness and mass matrices as well as member consistent load vector.

Vibration of plate and shell structures using triangular finite elements

1967 ◽  
Vol 2 (1) ◽  
pp. 73-83 ◽  
Author(s):  
R Dungar ◽  
R T Severn ◽  
P R Taylor
Keyword(s):  
Stiffness Matrix ◽  
Numerical Solutions ◽  
Mass Matrix ◽  
Arch Dam ◽  
Mode Shapes ◽  
Constant Thickness ◽  
Experimental Frequency ◽  
Single Plane ◽  
Stiffness Matrices ◽  
Mass Matrices

Mass and stiffness matrices are obtained for a general-triangle element and for a right-angled-triangle element. Both bending and in-plane actions are considered, although no coupling is assumed, and the matrices relating to bending actions are obtained independently of those relating to in-plane actions. Coupling is introduced, unless all the elements lie in a single plane, when the transformation from local to global co-ordinates is made. In deriving the stiffness matrices assumptions have been made about the form of the stress components within, and on the boundaries of, the element, together with assumptions about the form of the displacement components on the boundary of the element only. The commonly made assumptions in the derivation of stiffness matrices relate to the form of the displacement components not only on the boundary but throughout the element. In order to derive satisfactory mass matrices it is necessary to assume the form of the displacement components throughout the element. For the right-angled-triangle mass matrices these displacement components have been assumed independently of the assumed boundary displacements needed for the stiffness matrix. For the general-triangle mass matrix, however, the displacements throughout the element have been made consistent with the boundary displacements which were needed for the stiffness matrix. Numerical results are given for the first few natural frequencies of a square simply supported slab and a square encastré slab. Comparison with accepted values shows that the finite-element values are accurate, and convergent as the element size is reduced. For the same number of elements it is indicated that general triangles give a more accurate solution than right-angled triangles, probably because of the more satisfactory derivation of the mass matrix for the general triangle. This advantage is offset, however, by the greater computation time required by general triangles. Calculated and experimental frequency values are also given for a single-curvature arch dam of constant thickness. Mode shapes are not given in any of the numerical solutions although they are produced as an integral part of the computer programme.

Progressive failure mechanism in granular materials subjected to an alternant active and passive trapdoor

2021 ◽  
Vol 28 ◽  
pp. 100529
Author(s):  
Yu Zhao ◽  
Quanmei Gong ◽  
Yaojie Wu ◽  
Zhiyao Tian ◽  
Shunhua Zhou ◽  
...  
Keyword(s):  
Granular Materials ◽  
Failure Mechanism ◽  
Progressive Failure

scholarly journals Design of plate and screw anchors in dense sand: failure mechanism, capacity and deformation

2019 ◽  
Vol 92 ◽  
pp. 16010
Author(s):  
Benjamin Cerfontaine ◽  
Jonathan Knappett ◽  
Michael Brown ◽  
Aaron Bradshaw
Keyword(s):  
Shear Stress ◽  
Stress Distribution ◽  
Failure Mechanism ◽  
Progressive Failure ◽  
Vertical Direction ◽  
Shear Plane ◽  
Design Methods ◽  
Embedment Depth ◽  
Limiting State ◽  
Dense Sand

Plate and screw anchors provide a significant uplift capacity and have multiple applications in both onshore and offshore geotechnical engineering. Uplift design methods are mostly based on semi-empirical approaches assuming a failure mechanism, a normal and a shear stress distribution at failure and empirical factors back-calculated against experimental data. However, these design methods are shown to under- or overpredict most of the existing larger scale experimental tests. Numerical FE simulations are undertaken to provide new insight into the failure mechanism and stress distribution which should be considered in anchor design in dense sand. Results show that a conical shallow wedge whose inclination to the vertical direction is equal to the dilation angle is a good approximation of the failure mechanism in sand. This shallow mechanism has been observed in each case for relative embedment ratios (depth/diameter) ranging from 1 to 9. However, the stress distribution varies non-linearly with depth, due to the soil deformability and progressive failure. A sharp peak of normal and shear stress can be identified close to the anchor edge, before a gradual decrease with increasing distance along the shear plane. The peak stress magnitude increases almost linearly with embedment depth at larger relative embedment ratios. Although further research is necessary, these results lay the basis for the development of a new generation of design criteria for determining anchor capacity at the ultimate limiting state.

A Method for Use of Cyclic Symmetry Properties in Analysis of Nonlinear Multiharmonic Vibrations of Bladed Disks

2004 ◽  
Vol 126 (1) ◽  
pp. 175-183 ◽  
Author(s):  
E. P. Petrov
Keyword(s):  
High Efficiency ◽  
Equations Of Motion ◽  
Linear Part ◽  
Forced Response ◽  
Mode Shapes ◽  
Solution Technique ◽  
Disk Model ◽  
Sector Model ◽  
Bladed Disk ◽  
Symmetry Properties

An effective method for analysis of periodic forced response of nonlinear cyclically symmetric structures has been developed. The method allows multiharmonic forced response to be calculated for a whole bladed disk using a periodic sector model without any loss of accuracy in calculations and modeling. A rigorous proof of the validity of the reduction of the whole nonlinear structure to a sector is provided. Types of bladed disk forcing for which the method may be applied are formulated. A multiharmonic formulation and a solution technique for equations of motion have been derived for two cases of description for a linear part of the bladed disk model: (i) using sector finite element matrices and (ii) using sector mode shapes and frequencies. Calculations validating the developed method and a numerical investigation of a realistic high-pressure turbine bladed disk with shrouds have demonstrated the high efficiency of the method.

Free Flexural Vibrations Response of Composite Mindlin Plates or Panels With a Centrally Bonded Symmetric Double Lap Joint (or Symmetric Double Doubler Joint)

2005 ◽  
Author(s):  
U. Yuceoglu ◽  
O. Gu¨vendik ◽  
V. O¨zerciyes
Keyword(s):  
Natural Frequencies ◽  
Mode Shapes ◽  
Solution Technique ◽  
Shear Stresses ◽  
Lap Joint ◽  
Adhesive Layers ◽  
Present Solution ◽  
Flexural Vibrations ◽  
Support Conditions ◽  
Interpolation Polynomials

The present study is concerned with the “Free Flexural Vibrations Response of Composite Mindlin Plates or Panels with a Centrally Bonded Symmetric Double Lap Joint (or Symmetric Double Doubler Joint). The plate “adherends” and the plate “doublers” are considered as dissimilar, orthotropic “Mindlin Plates” with the transverse and the rotary moments of inertia. The relatively, very thin adhesive layers are taken into account in terms of their transverse normal and shear stresses. The mid-center of the bonded region of the joint is at the mid-center of the entire system. In order to facilitate the present solution technique, the dynamic equations of the plate “adherends” and the plate “doublers” with those of the adhesive layers are reduced to a set of the “Governing System of First Order ordinary Differential Equations” in terms of the “state vectors” of the problem. This reduced set establishes a “Two-Point Boundary Value Problem” which can be numerically integrated by making use of the “Modified Transfer Matrix Method (MTMM) (with Interpolation Polynomials)”. In the adhesive layers, the “hard” and the “soft” adhesive cases are accounted for. It was found that the adhesive elastic constants drastically influence the mode shapes and their natural frequencies. Also, the numerical results of some parametric studies regarding the effects of the “Position Ratio” and the “Joint Length Ratio” on the natural frequencies for various sets of support conditions are presented.

scholarly journals Stochastic Modal Models of Slender Uncertain Curved Beams Preloaded Through Clamping

2012 ◽  
Author(s):  
Javier Avalos ◽  
Lanae A. Richter ◽  
X. Q. Wang ◽  
Raghavendra Murthy ◽  
Marc P. Mignolet
Keyword(s):  
Stochastic Model ◽  
Stiffness Matrix ◽  
Natural Frequencies ◽  
Simulated Data ◽  
Mode Shapes ◽  
Curved Beams ◽  
Shape Information ◽  
Final Shape ◽  
Modal Model ◽  
Clamped Beams

This paper addresses the stochastic modeling of the stiffness matrix of slender uncertain curved beams that are forced fit into a clamped-clamped fixture designed for straight beams. Because of the misfit with the clamps, the final shape of the clamped-clamped beams is not straight and they are subjected to an axial preload. Both of these features are uncertain given the uncertainty on the initial, undeformed shape of the beams and affect significantly the stiffness matrix associated with small motions around the clamped-clamped configuration. A modal model using linear modes of the straight clamped-clamped beam with a randomized stiffness matrix is employed to characterize the linear dynamic behavior of the uncertain beams. This stiffness matrix is modeled using a mixed nonparametric-parametric stochastic model in which the nonparametric (maximum entropy) component is used to model the uncertainty in final shape while the preload is explicitly, parametrically included in the stiffness matrix representation. Finally, a maximum likelihood framework is proposed for the identification of the parameters associated with the uncertainty level and the mean model, or part thereof, using either natural frequencies only or natural frequencies and mode shape information of the beams around their final clamped-clamped state. To validate these concepts, a simulated, computational experiment was conducted within Nastran to produce a population of natural frequencies and mode shapes of uncertain slender curved beams after clamping. The application of the above concepts to this simulated data led to a very good to excellent matching of the probability density functions of the natural frequencies and the modal components, even though this information was not used in the identification process. These results strongly suggest the applicability of the proposed stochastic model.

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