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Elastic Plate (elastic + plate)

Distribution by Scientific Domains

Engineering	44%

Selected Abstracts

Crustal underplating and its implications for subsidence and state of isostasy along the Ninetyeast Ridge hotspot trail

GEOPHYSICAL JOURNAL INTERNATIONAL, Issue 2 2000
Ingo Grevemeyer
Recent seismic field work has revealed high lower-crustal velocities under Ninetyeast Ridge, Indian Ocean, indicating the presence of crustal underplating (Grevemeyer et al. 2000). We used results from Ocean Drilling Program (ODP) drill cores and cross-spectral analysis of gravity and bathymetric data to study the impact of the underplating body on the subsidence history and the mode of isostatic compensation along Ninetyeast Ridge. Compared with the adjacent Indian basin, the subsidence of Ninetyeast Ridge is profoundly anomalous. Within the first few millions of years after crustal emplacement the ridge subsided rapidly. Thereafter, however, subsidence slowed down significantly. The most reliable model of isostasy suggests loading of a thin elastic plate on and beneath the seafloor. Isostatic compensation of subsurface loading occurs at a depth of about 25 km, which is in reasonably good agreement with seismic constraints. Subsurface loading is inherently associated with buoyant forces acting on the lithosphere. The low subsidence may therefore be the superposition of cooling of the lithosphere and uplift due to buoyant material added at the base of the crust. A model including prolonged crustal growth in the form of subcrustal plutonism may account for all observations. [source]

A simplified analysis of interface failure under compressive normal stress and monotonic or cyclic shear loading

INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 4 2005
Zenon Mróz
Abstract Interface damage and delamination is usually accompanied by frictional slip at contacting interfaces under compressive normal stress. The present work is concerned with an analysis of progressive interface failure using the cohesive crack model with the critical stress softening and frictional traction present at the contact. Both monotonic and cyclic loadings are considered for anti-plane shear of an elastic plate bonded to a rigid substrate by means of cohesive interface. An analytical solution can be obtained by neglecting the effect of minor shear stress component. The analysis of progressive delamination process revealed three solution types, namely: short, medium and long plate solutions. The long plate solution was obtained under an assumption of quasistatic progressive growth of the delamination zone. In view of snap back response, the quasistatic deformation process cannot be executed by either traction or displacement control. The states of frictional slip accompanied by shake down or incremental failure are distinguished in the case of cyclic loading, related to load amplitude and structural dimensions. The analysis provides a reference solution for numerical treatment of more complex cases. Copyright © 2005 John Wiley & Sons, Ltd. [source]

Extension of the Griffith's fracture criteria to saturated clays

INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 4 2003
K.M. Dégué
Abstract Inglis [1] has solved the problem of distribution of stress in an elastic plate around an elliptical hole. His works clarify the role of cracks in the failure of an elastic material. However, his solution cannot be applied to saturated clay because he considers only total stresses, while, in saturated clay, the criterion of rupture should be expressed in terms of effective and not total stresses. The solution of Atkinson and Craster [2] using Biot's poroelasticity theory, shows that there is no high pore pressure in the vicinity of the crack tips for saturated clay. The major difference between this approach and the Biot's theory of is that, in saturated clay, strain is a function of the variation of the effective stress [3], while, in poroelastic media, strain is only a function of the variation of the total stress [4, Equation 2.2]. Also in their solution there is continuity between the pore fluid and the inner fluid in the crack. Their solution is valid for poroelastic media involving a movement of the pore fluid. In our solution there is no movement of the pore fluid (Undrained condition). In this paper we have solved the same problem as Inglis [1], but for the particular case of saturated clay obeying elastic law. By solving this problem we obtained the expressions for pore pressure, effective stress, total stress and displacements. The results show that not only the total stress but also the pore pressure and the effective stress are also high in the vicinity of the crack tips. A new failure criterion, based on Griffith's strain energy principle [5] and maximum tensile stress [6], valid for saturated clay is developed in this paper. Copyright © 2003 John Wiley & Sons, Ltd. [source]

An efficient co-rotational formulation for curved triangular shell element

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 9 2007
Zhongxue Li
Abstract A 6-node curved triangular shell element formulation based on a co-rotational framework is proposed to solve large-displacement and large-rotation problems, in which part of the rigid-body translations and all rigid-body rotations in the global co-ordinate system are excluded in calculating the element strain energy. Thus, an element-independent formulation is achieved. Besides three translational displacement variables, two components of the mid-surface normal vector at each node are defined as vectorial rotational variables; these two additional variables render all nodal variables additive in an incremental solution procedure. To alleviate the membrane and shear locking phenomena, the membrane strains and the out-of-plane shear strains are replaced with assumed strains in calculating the element strain energy. The strategy used in the mixed interpolation of tensorial components approach is employed in defining the assumed strains. The internal force vector and the element tangent stiffness matrix are obtained from calculating directly the first derivative and second derivative of the element strain energy with respect to the nodal variables, respectively. Different from most other existing co-rotational element formulations, all nodal variables in the present curved triangular shell formulation are commutative in calculating the second derivative of the strain energy; as a result, the element tangent stiffness matrix is symmetric and is updated by using the total values of the nodal variables in an incremental solution procedure. Such update procedure is advantageous in solving dynamic problems. Finally, several elastic plate and shell problems are solved to demonstrate the reliability, efficiency, and convergence of the present formulation. Copyright © 2007 John Wiley & Sons, Ltd. [source]

Simulation of Rayleigh waves in cracked plates

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 1 2007
M. T. Cao
Abstract The aim of this paper is to develop new numerical procedures to detect micro cracks, or superficial imperfections, in thin plates using excitation by Rayleigh waves. We shall consider a unilateral contact problem between the two sides of the crack in an elastic plate subjected to suitable boundary conditions in order to reproduce a single Rayleigh wave cycle. An approximate solution of this problem will be calculated by using one of the Newmark methods for time discretization and a finite element method for space discretization. To deal with the nonlinearity due to the contact condition, an iterative algorithm involving one multiplier will be used; this multiplier will be approximated by using Newton's techniques. Finally, we will show numerical simulations for both cracked and non-cracked plates. Copyright © 2006 John Wiley & Sons, Ltd. [source]

Weak solutions for time-dependent boundary integral equations associated with the bending of elastic plates under combined boundary data

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 7 2004
Igor Chudinovich
Abstract The existence, uniqueness, stability, and integral representation of distributional solutions are investigated for the equations of motion of a thin elastic plate with a combination of displacement and moment-stress components prescribed on the boundary. Copyright © 2004 John Wiley & Sons, Ltd. [source]

On the vibrations of a plate with a concentrated mass and very small thickness

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 1 2003
D. Gómez
Abstract We consider the vibrations of an elastic plate that contains a small region whose size depends on a small parameter ,. The density is of order O(,,m) in the small region, the concentrated mass, and it is of order O(1) outside; m is a positive parameter. The thickness plate h being fixed, we describe the asymptotic behaviour, as ,,O, of the eigenvalues and eigenfunctions of the corresponding spectral problem, depending on the value of m: Low- and high-frequency vibrations are studied for m>2. We also consider the case where the thickness plate h depends on ,; then, different values of m are singled out. Copyright © 2003 John Wiley & Sons, Ltd. [source]

Optimal placement of distributed actuators for a controlled smart elastic plate

PROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2003
F. Seeger
The performance and the efficiency of smart structures controlled by piezoelectric wafers decisively depend on the locations of the actuators and sensors. For the evaluation and testing of time consuming numerical optimisation techniques, which are currently a part of our research, benchmark examples are required. As such a benchmark example a simply supported plate structure is inverstigated, where the active controlled behaviour can still be described analytically. In the paper the optimisation algorithm is briefly described and the results of a typical example are presented. [source]