Plate Bending

Detecting and locating damage in structural components and joints that have high feature densities and complex geometry is a difficult problem in the field of structural health monitoring (SHM). Active propagation of diagnostic waves is one approach that is used to detect damage. But small cracks and damage are difficult to detect because they have a small effect on the propagating waves as compared to the effects the complex geometry itself which causes dispersion and reflection of waves. Another limitation of active wave propagation is that pre-damage data is required for every sensor-actuator combination, and a large number of sensors might be needed to detect small cracks on large structures. Overall, the problem of detecting damage in complex geometries is not well investigated in the field of SHM. Nevertheless, the problem is important because damage often initiates at joints and locations where section properties change.

The nonlinear bending of thin wires is a challenging topic in several applications where the final geometry of the wire after bending and springback has to be known. Typical examples are tyre manufacturing, helical spring design, spectacles frames. In order to develop analytical models able to set bending parameters for a required final shape of the wire, both account material behaviour (during the loading and unloading phases with springback effect) and geometrical nonlinearity have to be considered. In the case of plates bending, many analytical and numerical models are available in the literature, offering an accurate solution to this problem. However, the bending of thin wires could still be the subject of discussion and research. In this paper a new analytical model was developed, starting from the models available in the literature, in order to provide the designer with a simple model to predict the final shape of a wire by using mathematical codes. The model allows to predict with a higher level of accuracy the final shape of wires having different cross-sections after nonlinear bending. Since Bernoulli's hypothesis is assumed, the model can be used in all the applications where the material behaviour of the wire guarantees that plane cross sections of the wire will remain plane after rotation due to bending, with negligible errors from the engineering point of view.

Two noncrimp 3D woven carbon fibre composites (through thickness angle interlock) of binder volume fractions 3% and 6% were characterised for their response to applied deformation. Experiments were performed at quasi static, medium and high strain rates under a large variety of load cases (tension in warp/weft direction, interlaminar/intralaminar shear, through thickness tension/compression, 3-point bending and plate bending). During the study, novel experimental methods were developed in order to address several challenges specific to 3D composite materials. The results show that, while the different binder volume fractions of 3% and 6% have only a small effect on the in-plane stiffness (warp and weft direction), its effect on the delamination resistance in plate bending experiments is considerable. This is a very important result for the use of these materials in the future. The availability, in previous publications, of complementary data for the matrix and the interface between matrix pockets and fibre bundles makes the comprehensive data set a generically useful reference for hierarchical numerical modelling strategies.

This is the first of a two-part paper on plate bending elements with shear effects included. This paper presents a new three-node, nine-d.0.f. triangular plate bending element valid for the analysis of thick to thin plates. The element, called DKMT, has a proper rank (contains no spurious zero-energy modes), passes the patch test for thin and thick plates in an arbitrary mesh and is free of shear locking. Very good results have been obtained for thin and thick plates by the element. An extended DKQ element for thick-plate bending analysis is evaluated in Part ILZ4 Elements based on Reissner-Mindlin's theory"

In this paper, a node-based smoothed finite element method (NS-FEM) using 3-node triangular elements is formulated for static, free vibration and buckling analyses of Reissner-Mindlin plates. The discrete weak form of the NS-FEM is obtained based on the strain smoothing technique over smoothing domains associated with the nodes of the elements. The discrete shear gap (DSG) method together with a stabilization technique is incorporated into the NS-FEM to eliminate transverse shear locking and to maintain stability of the present formulation. A so-called node-based smoothed stabilized discrete shear gap method (NS-DSG) is then proposed. Several numerical examples are used to illustrate the accuracy and effectiveness of the present method.

A finite element template is a parametrized algebraic form that reduces to specific finite elements by setting numerical values to the free parameters. Following an outline of high performance elements, templates for Kirchhoff Plate-Bending Triangles (KPT) with 3 nodes and 9 degrees of freedom are studied. A 37-parameter template is constructed using the Assumed Natural Deviatoric Strain (ANDES) approach. Specialization of this template includes well known elements such as DKT and HCT. The question addressed here is: can these parameters be selected to produce high performance elements? The study is carried out by staged application of constraints on the free parameters. The first stage produces element families satisfying invariance and aspect ratio insensitivity conditions. Application of energy balance constraints produces specific elements. The performance of such elements in a preliminary set of benchmark tests is reported.

A finite element template is a parametrized algebraic form that reduces to specific finite elements by setting numerical values to the free parameters. Following an outline of high performance elements, templates for Kirchhoff Plate-Bending Triangles (KPT) with 3 nodes and 9 degrees of freedom are studied. A 37-parameter template is constructed using the Assumed Natural Deviatoric Strain (ANDES) approach. Specialization of this template includes well known elements such as DKT and HCT. The question addressed here is: can these parameters be selected to produce high performance elements? The study is carried out by staged application of constraints on the free parameters. The first stage produces element families satisfying invariance and aspect ratio insensitivity conditions. Application of energy balance constraints produces specific elements. The performance of such elements in a preliminary set of benchmark tests is reported.

Clay bodies exhibit pyroplasticity when they are fired. Basically they get soft again in the heat of the kiln and can deform under their own weight. This property is especially important when firing products with very low porosity like porcelain tiles, due their content in melting materials. In this way, five raw materials, a kaolin, a talc, an albite, a phyllite and a clay were used in a study to form porcelain tile pastes resistant to pyroplasticity. After raw materials analysis (XRF and XRD), a mixture design with constraint limits was used to compose the pastes, resulting in 13 compositions (five factors and one centroid). All compositions were mixed, wet grounded (<44 m), dried and pressed (450 kgf/cm 2 ) in rectangular plates (10 cm × 5 cm). The pyroplasticity was determined by the measure of the plate bending caused by temperature variation in an industrial roller kiln. All results were analyzed using response surfaces with data obtained by analysis of variance (ANOVA).

Finite element method (FEM) Smoothed finite element method (SFEM) Upper bound Lower bound Global error Polygonal a b s t r a c t This paper presents a node-based smoothed finite element method (NS-FEM) for upper bound solutions to solid mechanics problems using a mesh of polygonal elements. The calculation of the system stiffness matrix is performed using strain smoothing technique over the smoothing cells associated with nodes, which leads to line integrations along the edges of the smoothing cells. The numerical results demonstrated that the NS-FEM possesses the following properties: (1) upper bound in the strain energy of the exact solution when a reasonably fine mesh is used; (2) well immune from the volumetric locking;

In this work a meshless method for the analysis of bending of thin homogeneous plates is presented. This meshless method is based on the use of radial basis functions to build an approximation of the general solution of the partial differential equations governing the Kirchhoff plate bending problem. In order to obtain a symmetric and non-singular linear equation system the Hermite collocation method is used. To assess the formulation a series of plates with different boundary conditions are analysed. Comparisons are made with other results available in the literature. Copyright © 2001 John Wiley & Sons, Ltd.

In this paper, the coupling effect of extension and bending in functionally graded plate subjected to transverse loading for Kirchhoff-Love plate theory equations is studied. The material properties of the FG plates are assumed to vary continuously throughout the thickness direction of the layer according to sigmoid distribution of the volume fractions of constituents. The two plate functionals are used which are developed by Gâteaux differential and potential operator concept. A layer wise, isoparametric, mixed finite element approach was used and results of two different quadrilateral elements, one considering the membrane forces and the other one not, were compared by an analytical study. Finally, for different composition profiles the effect of variations of the Young's moduli and of variations volume fraction index to dimensionless displacement, strain and stress values are studied.

The validity and applicability of a high-level sim-6 ulation approach of radio-frequency microelectromechanical-7 system (RF-MEMS) devices, based on a library of analytical 8 compact models of elementary MEMS components, are investi-9 gated through an extensive comparison between simulation re-10 sults and measurements of some representative devices (variable 11 capacitors and series ohmic switches). The in-house developed 12 simulation tool is implemented in a standard IC simulation envi-13 ronment supporting behavioral description capabilities. The de-14 vices are built in a silicon substrate technology with suspended 15 gold membranes. We analyze the mechanical, electrical, and RF 16 response of the devices. The RF behavior is modeled by extracting 17 a lumped element network from measured S-parameters (scatter-18 ing-parameters) to account for parasitic effects and by wrapping 19 this network around the intrinsic MEMS device simulated with the 20 compact models. We show that an accuracy within 5% is obtained 21 in all considered physical domains and conditions, provided that 22 some effective parameters (including the residual air gap in the 23 actuated state and the RF parasitic elements) are properly ex-24 tracted from measurements and accounted for in the simulations. 25 The main factors limiting the model's predictive capability are 26 due to process nonidealities, such as plate bending due to residual 27 stress gradient, oxide charging, surface roughness, and suspended 28 membrane thickness variations, rather than for instance in-plane 29 geometric process variations. [2009-0266] 30

This paper presents a new formulation for thin-walled beams that includes cross-section deformation. The kinematic description of the beam emanates from the geometrically exact Reissner-Simo beam theory and is enriched with arbitrary cross-section deformation modes complying with Kirchhoff's assumption. The inclusion of these deformation modes makes it possible to capture the cross-section in-plane distortion, wall (plate) transverse bending and out-of-plane (warping), which leads to a computationally efficient numerical implementation. Several illustrative numerical examples are presented and discussed, showing that the resulting beam finite element leads to solutions that are in very good agreement with those obtained with standard shell finite elements, albeit involving much less degrees-of-freedom.

The healing process of bone fractures can be monitored by a measurement of the osteosynthesis plate bending. An electrical resonant circuit consisting of a coil with a magnetostrictive Galfenol core and a capacitance enables an indirect wireless measurement of the plate bending. The Galfenol core is manufactured with a thin film technology using a Galfenol Fe 83 Ga 17 alloy. The sensor has a quit good linear resonant frequency-force characteristic. Both, time and frequency domain measurement techniques for the sensor, use an external measurement coil. In the frequency domain the transformed sensor impedance is evaluated and the resonance frequency is determined by a local extremum. In the time domain a short energizing sinus pulse is transmitted, the sensor response is received and a frequency counting, Fourier or Wavelet technique is used for resonance frequency detection.

We present a Lagrange multiplier based substructuring method for solving iteratively large-scale systems of equations arising from the finite element discretization of static and dynamic plate bending problems. The proposed method is essentially an extension of the FETI domain decomposition algorithm to fourth-order problems. The main idea is to enforce exactly the continuity of the transverse displacement field at the substructure corners throughout the preconditioned conjugate projected gradient iterations. This results in a two-level FETI substructuring method where the condition number of the preconditioned interface problem does not grow with the number of substructures, and grows at most polylogatithmically with the number of elements per substructure. These theoretically proven optimal convergence
properties of the new FETI method are numerically demonstrated for several finite element plate bending static and transient problems. The two-level iterative solver presented in this paper is applicable to a large family of biharmonic time-independent as well as time-dependent systems. It is also extendible to shell problems.

This paper promotes a novel numerical approach to static, free vibration and buckling analyses of laminated composite plates by an edge-based smoothed finite method (ES-FEM). In the present ES-FEM formulation, the system stiffness matrix is established by using the strain smoothing technique over the smoothing domains associated with the edges of the triangular elements. A discrete shear gap (DSG3) technique without shear locking is combined into the ES-FEM to give a so-called edge-based smoothed discrete shear gap method (ES-DSG3) for analysis of laminated composite plates. The present method uses only linear interpolations and its implementation into finite element programs is quite simple. Numerical results for analysis of laminated composite plates show that the ES-DSG3 performs quite well compared to several other published approaches in the literature.

This paper deals with a single server working vacation queueing model with multiple types of server breakdowns. In a working vacations queueing model, the server works at a different rate instead of being completely idle during the vacation period; the arrival rate varies according to the server's status. It is assumed that the server is subject to interruption due to multiple types of breakdowns and is sent immediately for repair. Each type of breakdown requires a finite random number of stages of repair. The life time of the server and the repair time of each phase are assumed to be exponentially distributed. We propose a matrix-geometric approach for computing the stationary queue length distribution. Various performance indices namely the expected length of busy period, the expected length of working vacation period, the mean waiting time and average delay, etc. are established. In order to validate the analytical approach, by taking illustration, we compute numerical results. The sensitivity analysis is also performed to explore the effect of different parameters.

SUMMARY This paper focuses on the application of orthotropi c plate bending theory to stiffened plating. Schade &#39;s design charts for rectangular plates are extended to the case where t he boundary contour is clamped, which is almost tot ally incomplete in the afore mentioned charts. A numerical solution for the clamped orthotropic p late equation is obtained. The Rayleigh-Ritz

This is the first of a two-part paper on plate bending elements with shear effects included. This paper presents a new three-node, nine-d.0.f. triangular plate bending element valid for the analysis of thick to thin plates. The element, called DKMT, has a proper rank (contains no spurious zero-energy modes), passes the patch test for thin and thick plates in an arbitrary mesh and is free of shear locking. Very good results have been obtained for thin and thick plates by the element. An extended DKQ element for thick-plate bending analysis is evaluated in Part ILZ4 Elements based on Reissner-Mindlin's theory"

A node-based smoothed finite element method (NS-FEM) was recently proposed for the solid mechanics problems. In the NS-FEM, the system stiffness matrix is computed using the smoothed strains over the smoothing domains associated with nodes of element mesh. In this paper, the NS-FEM is further extended to more complicated visco-elastoplastic analyses of 2D and 3D solids using triangular and tetrahedral meshes, respectively. The material behavior includes perfect visco-elastoplasticity and visco-elastoplasticity with isotropic hardening and linear kinematic hardening. A dual formulation for the NS-FEM with displacements and stresses as the main variables is performed. The von-Mises yield function and the Prandtl–Reuss flow rule are used. In the numerical procedure, however, the stress variables are eliminated and the problem becomes only displacement-dependent. The numerical results show that the NS-FEM has higher computational cost than the FEM. However the NS-FEM is much more accurate than the FEM, and hence the NS-FEM is more efficient than the FEM. It is also observed from the numerical results that the NS-FEM possesses the upper bound property which is very meaningful for the visco-elastoplastic analyses which almost have not got the analytical solutions. This suggests that we can use two models, NS-FEM and FEM, to bound the solution, and can even estimate the global relative error of numerical solutions.

This article describes the methodology and presents results of a study of the evaluation of the post-cracking performance of shotcrete reinforced with high modulus polymeric fibers using two panel-based tests: the Plate Bending Test of EFNARC, and the Round Determinate Panel Test proposed by Bernard. A plain shotcrete and a steel fiber reinforced shotcrete have also been tested for comparison.

We analyze the discontinuous Petrov-Galerkin (DPG) method with optimal test functions when applied to solve the Reissner-Mindlin model of plate bending. We prove that the hybrid variational formulation underlying the DPG method is well-posed (stable) with a thickness-dependent constant in a norm encompassing the L 2 -norms of the bending moment, the shear force, the transverse deflection and the rotation vector. We then construct a numerical solution scheme based on quadrilateral scalar and vector finite elements of degree p. We show that for affine meshes the discretization inherits the stability of the continuous formulation provided that the optimal test functions are approximated by polynomials of degree p + 3. We prove a theoretical error estimate in terms of the mesh size h and polynomial degree p and demonstrate numerical convergence on affine as well as non-affine mesh sequences.

We present a new plate bending triangular finite element. It is developed in perspective to building shell elements. Its formulation uses concepts related to the deformation approach, the fourth fictitious node, the static condensation and analytic integration. It is based on the assumptions of the theory of thin plates (Kirchhoff theory). The approach has resulted in a bending plate finite element (HIMEUR) competitive, robust and efficient.

A shear locking free isoparametric three-node triangular plate bending element, KEYA, is developed. Reissner/Mindlin theory that incorporates transverse shear deformation is assumed in the plate formulations. Numerical results include patch tests, convergence of transverse displacement and stress resultants, and variations of them for various parametric effects on cantilever, simply supported and clamped plates.

Current debates on the existence of mantle plumes largely originate from interpretations of supposed signatures of plume-induced surface topography that are compared with predictions of geodynamic models of plume-lithosphere interactions. These models often inaccurately predict surface evolution: in general, they assume a fixed upper surface and consider the lithosphere as a single viscous layer. In nature, the surface evolution is affected by the elastic-brittle-ductile deformation, by a free upper surface and by the layered structure of the lithosphere. We make a step towards reconciling mantle-and tectonic-scale studies by introducing a tectonically realistic continental plate model in large-scale plume-lithosphere interaction. This model includes (i) a natural free surface boundary condition, (ii) an explicit elastic-viscous(ductile)-plastic(brittle) rheology and (iii) a stratified structure of continental lithosphere. The numerical experiments demonstrate a number of important differences from predictions of conventional models. In particular, this relates to plate bending, mechanical decoupling of crustal and mantle layers and tension-compression instabilities, which produce transient topographic signatures such as uplift and subsidence at large (>500 km) and small scale (300-400, 200-300 and 50-100 km). The mantle plumes do not necessarily produce detectable large-scale topographic highs but often generate only alternating small-scale surface features that could otherwise be attributed to regional tectonics. A single large-wavelength deformation, predicted by conventional models, develops only for a very cold and thick lithosphere. Distinct topographic wavelengths or temporarily spaced events observed in the East African rift system, as well as over French Massif Central, can be explained by a single plume impinging at the base of the continental lithosphere, without evoking complex asthenospheric upwelling.

We have used body-wave modelling to determine the source parameters of 22 moderate to large earthquakes that have occurred along the Hikurangi subduction margin and elsewhere in the North Island of New Zealand since 1964. We have also included events from the Harvard CMT catalogue since 1977 as that catalogue contains smaller events than can be modelled with body waves. We have found that shallow earthquakes occurring in the back-arc Taupo Volcanic Zone and its extension to the north show predominantly normal faulting with nodal planes parallel to the regional fabric and T -axes indicating extension in a direction in agreement with geodetic measurements. A normal faulting solution for the 1974 Opunake earthquake is compatible with the mapping of active faults in the offshore Taranaki region, and the initiation depth of 17 km is close to the expected brittle–ductile transition for that area. Earthquakes within the subducted plate at the southwestern end of the margin are dominated by down-dip tension that is rotated towards the deepest part of the subducting plate. Further north, the events in the upper part of the Wadati–Benioff zone (<200 km) show pure down-dip tension, while this association is less obvious for the deeper events, suggesting that the aseismic part of the subducting slab inferred from plate reconstructions has reached the 670 km discontinuity. Normal faulting earthquakes associated with plate bending below the region of interplate contact occur along the length of the margin, while shallow normal faulting events also occur in the trench, indicating that some slab pull propagates to that region. We infer that large interplate earthquakes are not imminent because in other similar areas they are preceded by outer-rise compressional events that have not been recorded in the region in historical times. Slip vectors of interplate thrust earthquakes indicate that the oblique plate motion across the margin is fully partitioned; that is, the plate interface accommodates very little transcurrent motion, which is instead accommodated by faults in the overlying Australian Plate. Extensional geodetic strain has been measured across the margin in the northeast, which has been regarded as unusual in view of the plate convergence. We suggest that the topography at this part of the margin is too steep to be supported by the current horizontal forces due to friction on the plate interface. This may have occurred due to a reduction in friction because of the subduction of seamounts and the subsequent entrapment of sediments, this also being consistent with the idea of underplating at this part of the margin, or due to the subduction of less buoyant crust. Other margins, such as Japan and Mid-America, where there is known to be subduction of sediments, also show extension in the forearc. Compressional strain observed across the margin in the southwest is more usual for a convergent margin, but it does not show the partitioning we see in focal mechanisms. These data might only agree after the long-term compressional strain accumulation has been averaged over a complete seismic cycle. Large historical and palaeo-earthquakes have occurred along the length of the margin associated with deformation in both the axial and the coastal ranges. In addition, along the length of the margin the rate of recent interplate thrust activity is low compared to margins that have a high proportion of aseismic slip. These factors indicate that the entire length of this margin is capable of producing large earthquakes.

We propose two new boundary integral equation formulas for the biharmonic equation with the Dirichlet boundary data that arises from plate bending problems in R 2. Two boundary conditions, u and ∂u/∂n, usually yield a 2 × 2 non-symmetric matrix system of integral equations. Our new formulas yield scalar integral equations that can be handled more efficiently for theoretical and numerical purposes. In this paper we supply complete ellipticity and solvability analyses of our new formulas. Numerical experiments for simple Galerkin methods are also provided.

A finite element formulation is presented to model the dynamic as well as static response of laminated composite plates containing integrated piezoelectric sensors and actuators subjected to both mechanical and electrical loadings. The formulation is based on the classical laminated plate theory and Hamilton's principle. In this formulation, the mass and stiffness of the piezo-layers have been taken into account. A four-node non-conforming rectangular plate bending element is implemented for the analysis. A simple negative velocity feedback control algorithm coupling the direct and converse piezoelectric effects is used to actively control the dynamic response of an integrated structure through a closed control loop. The model is validated by comparison with existing results documented in the literature. Several numerical examples are presented. The influence of stacking sequence and position of sensors/actuators on the response of the plate is evaluated.

A new stiffened plate bending element for the vibration analysis of stiffened plate structures is presented. The element can include the stiffeners anywhere within the element. The method can be called the master element technique. By this method the geometry idealization error can be reduced considerably, because there is no need to make remarkable geometrical simplifications. The use of master

We applied an improved stress inversion method to a comprehensive data set of earthquake focal mechanisms to depict the pattern of crustal stress along the western convergent boundary of the Philippine Sea plate. Our results indicate that the crustal stress along the Ryukyu fore arc is segmented with boundaries at or near the places of seamount subduction, including the Tokara channel. An extensional stress regime is observed along the entire Ryukyu back arc, implying that back-arc rifting may have extended northward to Kyushu. A triangular area near the southernmost terminus of the Ryukyu arc is characterized by a unique stress signature. The eastern boundary of this Ryukyu-Taiwan Stress Transition coincides with the 123°E meridian where the Gagua ridge intercepts the Ryukyu trench; whereas its western boundary agrees remarkably well with the border between the postcollision and waning-collision domains in northern Taiwan. The Taiwan collision zone is dominated by compression that rotates locally according to the structural configuration of the Lukang Magnetization High (LMH), suggesting that the LMH may be critical in controlling the local stress distribution. The stress signature of the Luzon arc-Taiwan collision reaches as far south as 19.5°N. The tectonic stress along the Manila trench-Luzon fore arc is dominated by a complex regime of extension that cannot be explained by simple plate bending or in-slab membrane stress. Since this extensional regime is observed only south of ∼22°N, it probably marks the northern limit of the contemporary boundary between the subduction along the Manila trench and the collision in Taiwan.

For subduction to occur, plates must bend and slide past overriding plates along fault zones. Because the lithosphere is strong, significant energy is required for this deformation to occur, energy that could otherwise be spent deforming the mantle. We have developed a finite element representation of a subduction zone in which we parameterize the bending plate and the fault zone using a viscous rheology. By increasing the effective viscosity of either the plate or the fault zone, we can increase the rates of energy dissipation within these regions and thus decrease the velocity of a plate driven by a given slab buoyancy. We have developed a simple physical theory that predicts this slowing by estimating a convecting cell's total energy balance while taking into account the energy required by inelastic deformation of the bending slab and shearing of the fault zone. The energy required to bend the slab is proportional to the slab's viscosity and to the cube of the ratio of its thickness to its radius of curvature.

In this paper, the linear free flexural vibration of cracked functionally graded material plates is studied using the extended finite element method. A 4noded quadrilateral plate bending element based on field and edge consistency requirement with 20 degrees of freedom per element is used for this study. The natural frequencies and mode shapes of simply supported and clamped square and rectangular plates are computed as a function of gradient index, crack length, crack orientation and crack location. The effect of thickness and influence of multiple cracks is also studied.

A constitutive model of bulk metallic glass (BMG) plasticity is developed which accounts for finitedeformation kinematics, the kinetics of free volume, strain hardening, thermal softening, rate-dependency and non-Newtonian viscosity. The model has been validated against uniaxial compression test data; and against plate bending experiments. The model captures accurately salient aspects of the material behavior including: the viscosity of Vitreloy 1 as a function of temperature and strain rate; the temperature and strain-rate dependence of the equilibrium free-volume concentration; the uniaxial compression stress-strain curves as a function of strain rate and temperature; and the dependence of shear-band spacing on plate thickness. Calculations suggest that, under adiabatic conditions, strain softening and localization in BMGs is due both to an increase in free volume and to the rise in temperature within the band. The calculations also suggest that the shear band spacing in plate-bending specimens is controlled by the stress relaxation in the vicinity of the shear bands.

This paper illustrates, through a worked out example, the application of finite element templates to construct high performance bending elements for vibration and buckling problems. The example focuses on the improvement of the mass and geometric stiffness matrices of plane beams. Similar methods can be used for Kirchhoff plate bending elements, but this material is omitted because of space constraints. The process interweaves classical tools: Fourier analysis and orthogonal polynomials, with newer ones: finite element templates and computer algebra systems. Templates are parametrized algebraic forms that uniquely characterize an element population by a "genetic signature" defined by the set of free parameters. Specific elements are obtained by assigning numeric values to the parameters. This freedom of choice can be used to design custom elements. For the beam example, Legendre polynomials are used to construct templates for the material stiffness, geometric stiffness and mass matrices. Fourier analysis carried out through symbolic computation searches for template signatures of mass and stiffness that deliver matrices with desirable attributes for specific target situations. Three objectives are noted: high accuracy for vibration and buckling analysis, wide separation of acoustic and optical branches, and low sensitivity to mesh distortion and boundary conditions. This paper examines in some detail only the first objective.

Bending of lithospheric plates at subduction zones is thought to be an important source of dissipation for convection in the Earth's mantle. However, the influence of bending on plate motion is uncertain. Here we use a variational description of mantle convection to show that bending strongly affects the direction of plate motion. Subduction of slabs and subsidence of oceanic lithosphere with age provide the primary driving forces. Dissipation is partitioned between plate bending and various sources of friction at plate boundaries and in the interior of the mantle due to viscous flow. We determine the poles of rotation for the Pacific and Nazca plates by requiring the net work to be stationary with respect to small changes in the direction of motion. The best fit to the observed rotation poles is obtained with an effective lithospheric viscosity of 6 × 10 22 Pa s. Bending of the Pacific plate dissipates roughly 40% of the energy released by subduction through the upper mantle.

The work presented here concerns the use of radial basis functions (RBFs) for the analysis of two dimensional elastostatic problems. The basic characteristic of the formulation is the definition of a global approximation for the variables of interest in each problem (the deflection for the plate bending problem and the stress function for the stretching plates) from a set of RBFs conveniently placed (but not necessarily in a regular manner) at the boundary and in the domain. Depending on the type of collocation chosen, non-symmetric or symmetric systems of linear equations are obtained. Comparisons are made with other results available in the literature.

In this paper, we establish the convergence of a nonconforming triangular Morley element for the plate bending problem for some degenerate meshes. An explicit bound for the interpolation error is derived for arbitrary triangular meshes without any assumptions. The optimal convergence rates of moment error and rotation error are derived for triangular meshes satisfying the maximal angle condition. Our results can also be extended to the three dimensional Morley element presented recently in . Finally, some numerical results are reported that confirm our theoretical results.

This paper presents an alternative alpha finite element method using triangular meshes (AαFEM) for static, free vibration and buckling analyses of laminated composite plates. In the AαFEM, an assumed strain field is carefully constructed by combining compatible strains and additional strains with an adjustable parameter α which can produce an effectively softer stiffness formulation compared to the linear triangular element. The stiffness matrices are obtained based on the strain smoothing technique over the smoothing domains and the constant strains on triangular sub-domains associated with the nodes of the elements. The discrete shear gap (DSG) method is incorporated into the AαFEM to eliminate transverse shear locking and an improved triangular element termed as AαDSG3 is proposed. Several numerical examples are then given to demonstrate the effectiveness of the AαDSG3.

A low-order thick and thin plate bending element is derived using bilinear approximations for the transverse deflection, the two rotations and the thickness change. The stress–strain relationships from three-dimensional elasticity are used without any modifications. In order to avoid locking and to improve the accuracy of the results eight enhanced strain modes are used. For an efficient implementation of the mixed element, orthogonal stress and strain functions are utilized. Although the element is a low-order finite element the numerical results for a series of standard test problems are excellent. Copyright © 2001 John Wiley & Sons, Ltd.

1] We have studied faulting associated with bending of the incoming oceanic plate along segments of Middle America and Chile subduction zones and its relationship to intermediate-depth intraslab seismicity and slab geometry. Multibeam bathymetry shows that bending-related faulting forms patterns made of sets of faults with orientations ranging from parallel to almost perpendicular to the trench axis. These fault patterns may change along a single subduction zone within along-strike distances of several hundred kilometers or less. Where available, near-trench intraplate earthquakes show normal-fault focal mechanisms consistent with mapped bending-related normal faults. The strike of bending-related faults in the incoming oceanic plate is remarkably similar to the strike of the nodal planes of intermediate-depth earthquakes for each segment of the study areas. This similarity in strike is observed even for faults oriented very oblique to the trench and slab strikes. Thus, in the studied subduction zones, results strongly support that many intraslab earthquakes do not occur along the planes of maximum shear within the slab and that much intermediate-depth seismicity occurs by reactivation of faults formed by plate bending near the trench. Furthermore, a qualitative relationship between trench faulting and intraslab seismicity is indicated by segments of the incoming plate with pervasive bend-faulting that correspond to segments of the slabs with higher intermediate-depth seismicity.

. The direct boundary element approach is applied to moderately thick plates di#erential operators, including the membrane-bending coupling terms. All the integral equations for geometrically non-linear plate bending problems are then obtained including the shear deformation e#ects. A linearization of these equations leads to the integral equations for the linear elastic stability analysis of plates. Numerical derivatives of the transversal displacement are avoided. Instead, direct di#erentiation of the integral equations for the transverse displacement is used leading to an hypersingular integral equation. Results are presented for linear bending using constant, linear, quadratic, cubic, and quartic boundary elements. Buckling problems are solved using constant boundary elements and domain cells, in order to avoid hypersingular integrals. 1 R. J. Marczak and C. S. de Barcellos 1 INTRODUCTION The development of a general boundary element approach for plate bending analysis is still ...