Bending Of Elastic Plates Research Articles

R-functions in problems of bending of three-layer plates

We study the application of the method of R-functions to the solution of problems of bending of elastic three-layer plates of arbitrary shape. We obtain new solution structures for plates that are freely supported over the whole boundary. We solve test problems and compare the experimental and theoretical results. All numerical results were obtained using the POLE programming system.

Highly Accurate Analysis for Thin Elastic Plate Bending Problem by Boundary Element Method. 1st Report. Regularization for Hyper-Singular Integral by Rigid Rotation Mode.

The boundary element method (BEM) for thin elastic plate bending analysis uses two different integral equations for the displacement and the slope. It is difficult to integrate the integral equation for rotation accurately, because the equation has hyper-singularity. In the present paper, these boundary integral equations are nomalized by the superposition of the rigid rotation mode. Through some numerical results of square plates under several boundary conditions, it is shown that unknown nodal values along the boundary are more accurately obtained that those of the usual methods, and the accuracy of deflections, moments and shear forces at internal points has been clearly improved.

A method using the reciprocal theorem to solve the bending of thin elastic semicircular plates

The bending of the thin elastic semicircular plates, because of its complicated boundary conditions, brings some difficulties, for us to obtain its solution. This paper applies, the reciprocal theorem to propose a general simple convenient method to obtain the transverse deflectional equations of the plates.

On Finite Twisting and Bending of Nonhomogeneous Anisotropic Elastic Plates

On Finite Twisting and Bending of Nonhomogeneous Anisotropic Elastic Plates

Application of complex path-independent integrals to problems of bending of thin elastic plates

Complex path-independent integrals have been already widely applied to problems of plane and antiplane elasticity for the determination of a variety of quantities of interest including stress intensity factors, loading intensities and the positions of geometrical characteristic lengths of singularities in the elastic field (like cracks, holes and inclusions). In this paper, we show that the same results apply also to the case of problems of thin isotropic elastic plates under bending where the complex-variable formulation is also valid. We make reference to the experimental methods which are appropriate for these integrals in an engineering environment and, finally, we apply this approach to the location of a circular hole in the problem of bending of a thin plate. Numerical results are also presented.

Theory of dynamic bending of thin elastic high nonhomogeneous plates

Primary bending motions of thin plates with an arbitrary hierarchy of layers are considered. Large differences in thicknesses. Young's moduli and sound velocities are taken into account in view of additional small parameters in 3-D equations of the theory of elasticity. Based on the asymptotical analysis the general approximate 2-D equations are deduced first. Then they are simplified and classified depending on asymptotical powers of the mentioned differences and locations of layers.

Analytical Solutions for In-Plane and Out-of-Plane Problems with Elliptic Hole or Elliptic Rigid Inclusion and Their Applications. 4th Report. Basic Theory for Isotropic and Anisotropic Plate Bending Problems.

This paper presents a unified analysis of plate bending problems due to classical plate theory containing an elliptic hole or elliptic rigid inclusion under singular point moments and point discrepancies of deflection and slope as well as applied moments and torque at infinity. The analogies existing between the mathematical formulations of the transverse bending of elastic plates and two-dimensional stress problems are used for analytical treatments.

Approximate determinations of the center of shear by use of the St. Venant solution for the flexure problem of plates of variable thickness

We extend a recent analysis of the shear center problem in the context of the linear theory of transverse bending of orthotropic elastic plates by an explicit comparison of results based on several differing definitions of the center of shear within the framework of the St. Venant flexure solution for the problem of orthotropic plates. We also consider transverse bending of anisotropic plates where we find a significant aspect ratio effect not present in the orthotropic, case, and the shear center problem for plates with combined midplane bending and stretching as a consequence of constitutive coupling.

Elementwise A Posteriori Error Estimation of Finite Element Solutins for Three-Dimensional Elastic Proflems and Plate Bending Problems.

An a posteriori error estimation method for finite element solutions for 3-dimensional elastic problems and plate bending problems is presented. The method is successfully applied to 3-dimensional elastic problems and plate bending problems. In order to decrease the computing time and memory use, error is estimated element by element. The major difficulty in the elemestwise error estimation technique is satisfying the self-equilibrium condition of applied forces in 3-dimensional problems and plate bending problems. These forces are mainly due to traction discontinuity on the element boundaries. The difficulty is circumvented by employing an elementwise optimal procedure. It is also shown that a very accurate stress solution can be obtained by adding estimated error to the original finite element solution.

On asymptotic expansions for the sixth-order linear theory problem of transverse bending of orthotropic elastic plates

We extend earlier considerations of the sixth-order linear theory problem of shear deformable orthotropic plates by a systematic analysis of the boundary layer problem along straight edges parallel to the directions of elastic symmetry of the plate. We extend the concept of ‘'soft'’ support as a condition for the smooth transition from the sixth-order theory to fourth-order theory in the limit of vanishing plate thickness to a concept of ‘almost soft’ support. Additionally, we obtain a generalized version of an earlier result concerning a system of boundary conditions for the differential equations of the classical fourth-order theory which is such that this fourth-order theory accounts for transverse shear deformation effects of the first order.

A higher-order plate theory with ideal finite element suitability

A variational tenth-order theory for stretching and bending of orthotropic elastic plates is proposed which lends itself perfectly to finite element formulations based upon C 0 and C −1 -continuous displacement approximations. The deformations due to all strain and stress components are accounted. The theory is derived from three-dimensional elasticity via a modified virtual work statement based upon independent displacement and transverse strain expansions through the thickness. The transverse displacement employs a special parabolic form while the in-plane displacements are taken to be linear. The issues of thickness-expansion related inconsistencies in the transverse shear strains and the transverse normal stress are resolved by the enforcement of physical stress boundary conditions and variationally consistent ‘weak’ transverse strain compatibility. The resulting transverse shear strains are parabolic, while the transverse normal strain varies cubically across the plate thickness. The variational principle yields seven equations of motion and exclusively Poisson-type edge boundary conditions. A qualitative assessment of the theory is carried out for the problem of static equilibrium involving an infinite plate under a sinusoidal normal pressure. A simple three-node plate element is then developed comparable in computational efficiency to its Mindlin-theory counterpart but which enables accurate computation of all displacement, strain and stress components for a wide range of the plate span-to-thickness ratio.

Was the coppermine homocline of northwestern Canada uplifted as part of a Middle Proterozoic forebulge

Application of the principles of elastic plate bending to subsurface geometric information and outcrop in northwestern Canada suggests that Proterozoic crust was loaded and deflected during orogenic activity between about 1.6 and 1.1 Ga. Exposed Hudsonian (ca. 1.8–2.0 Ga) basement separating younger but coeval stratigraphic sequences in the Coppermine Homocline on the west and Bathurst Inlet on the east can be explained as a forebulge associated with the loading.

Development of Simulator for Plate by Line-Heating Considering In-Plane Shrinkage

Plate bending is one of the most difficult techniques in shipbuilding and many investigations into the associated problems have been carried out. In this paper, associated problems have been carried out. In this paper, the development of a simulator for plate bending by line-heating is proposed. The simulation is based on a simplified non-linear elastic plate bending model. It was found that much improvement to the system was required. In-plane shrinkage was introduced, to select the best restraint conditions in FEM numerical calculation, and to construct an improved interface.

Regularized Boundary Integral Equation Formulations for Thin Elastic Plate Bending Analysis.

The boundary integral equations conventionally used for thin elastic plate bending analysis have the singularities of the Cauchy principal value order for which special care must be taken in numerical evaluation when the boundary is discretized by using the higher-order elements. In the present paper, the boundary integral equations are regularized up to an integrable order by using the subtracting and adding back technique. The obtained boundary integral equations both for deflection and rotation are weakly singular, and their discretized forms can be integrated accurately by the standard Gaussian quadrature formula. Numerical implementation of the resulting regularized integral equations is presented, and effectiveness of the proposed method is discussed through some numerical demonstrations.

Application of Boundary Integral Method to Continuous Plate Structures

Ship hulls are composed of complex plate structures. Such structures can be analyzed by analytical as well as numerical methods. Here it is demonstrated that boundary integrals can be used to analyze such structures by a seminumerical method. Boundary integrals have been used for analyzing single plate bending problems, and only recently have attempts been made to extend their use to complex plate structures. In this paper the Direct Boundary Integral Method for bending of thin elastic plates is extended to analysis of the continuous plate structures. The concepts of compatibility and equilibrium conditions along the common boundary have been imposed in conjunction with a boundary element formulation for each panel. Several examples of loading conditions are presented and compared with analytical solutions. The excellent agreement achieved illustrates the effectiveness of the extended formulation.

Smoothness of Elastic Potentials in the Theory of Bending of Thin Plates

The existence and uniqueness are discussed of a regular solution to a theory of bending of thin elastic plates with transverse shear deformation. The boundary integral equation method can be employed to handle such problems only after an essential modifications is operated, regarding the asymptotic behaviour of the solution

Similarity problems of the dynamic axisymmetric bending of nonlinearly elastic plates

Similarity problems of the dynamic axisymmetric bending of nonlinearly elastic plates

Notch mechanics for plane and thin plate bending problems

This paper describes the summary of notch mechanics based on the linear elasticity. The V-shaped notch with sharp or round corner and symmetric to the bisector is the object of this study. The plane elastic problem and thin plate bending problem are considered for free and fixed boundary conditions. The following matters are investigated: the stress distributions near the sharp corner; the general expression of the stress concentration at the round corner; the relationship between the intensity of corner and the stress concentration; and the stress intensity factor of a crack initiating from the notch tip. The notch mechanics is connected with the crack mechanics by the expression of stress intensity factor.

The bending of curvilinear plates by the finite difference method

The problem of linear elastic plate bending is formulated by use of the decomposition of the fourth order plate bending equation into coupled second order equations. Clamped and simply supported conditions are considered along either straight or curvilinear boundaries and, in particular, an exact formulation is provided for the simply supported condition at a curvilinear boundary. The finite difference method is employed, based on a rectangular difference net. This results in irregular points only being created along curvilinear boundaries and at positions of abrupt changes in the net grading. Where irregular points occur, use is made of local quadratic approximating functions to derive the required difference representations. Suitable strategies are presented for the avoidance of singularity in the local function derivations and for the minimisation of conditioning errors in the finite difference solution. The formulation is shown to be both economical and accurate for the solution of a test problem taking the form of a uniformly loaded elliptical plate.

Development of Simulator for Plate Bending by Line-Heating

The most characteristic work in shipbuilding industry is to bend thick-steel plates. It is often said that plate bending technique is one of the most difficult one.In order to solve those technological problems, a lot of investigations were conducted in the past 30 years in Japan. A series of universal press with multiple piston heads have been studied, in order to automate plate bending process. The other approach was contributed by 4th Subcommittee of the Systems Technology and Computer Application Committee. They proposed that such shipbuilding skills should systematically be analysed to be applicable for researches on Artificial Intelligence and Expert System.The aim of this paper in to develop a simulator for plate bending by Line-Heating. A Simplified non-linear elastic plate bending model is introduced instead of thermal elasto-plastic and large deformation analysis. Engineering work station is used in the main system and FEA is carried out in numerical calculation. And the system supports good interface. So user can understand plate bending intuitively and acquire know-how of it. The simulator is useful to a training facility for technicians.