Moving Loads on an Elastic Plate Strip

1974 ◽  
Vol 41 (3) ◽  
pp. 713-718 ◽  
Author(s):  
A. A. Adler ◽  
H. Reismann
Keyword(s):  
Plate Theory ◽  
Infinite Plate ◽  
Harmonic Component ◽  
Closed Form Solution ◽  
Form Solution ◽  
Elementary Functions ◽  
Transform Method ◽  
Line Load ◽  
Plate Strip ◽  
The Fourier Transform

The response of an infinite plate strip under an arbitrarily distributed transverse moving line load is determined. The line of application of the load is perpendicular to the infinite edges, and the load is assumed to propagate parallel to the infinite edges of the plate at constant speed. The problem is formulated as a boundary-value problem within the framework of a plate theory which includes the effects of shear deformation and rotatory inertia. A closed-form solution, in terms of elementary functions, is obtained for each harmonic component of the line load by the Fourier transform method in conjunction with contour integration.

scholarly journals FOURIER TRANSFORM METHODS FOR REGIME-SWITCHING JUMP-DIFFUSIONS AND THE PRICING OF FORWARD STARTING OPTIONS

2012 ◽  
Vol 15 (05) ◽  
pp. 1250037 ◽  
Author(s):  
ALESSANDRO RAMPONI
Keyword(s):  
Fourier Transform ◽  
Regime Switching ◽  
Closed Form Solution ◽  
Jump Diffusion ◽  
Form Solution ◽  
Transform Method ◽  
Finite State ◽  
Jump Diffusion Model ◽  
Log Price ◽  
The Fourier Transform

In this paper we consider a jump-diffusion dynamic whose parameters are driven by a continuous time and stationary Markov Chain on a finite state space as a model for the underlying of European contingent claims. For this class of processes we firstly outline the Fourier transform method both in log-price and log-strike to efficiently calculate the value of various types of options and as a concrete example of application, we present some numerical results within a two-state regime switching version of the Merton jump-diffusion model. Then we develop a closed-form solution to the problem of pricing a Forward Starting Option and use this result to approximate the value of such a derivative in a general stochastic volatility framework.

Design and finite element assessment of fully uncoupled multi-directional layups for delamination tests

2019 ◽  
Vol 54 (6) ◽  
pp. 773-790 ◽  
Author(s):  
Torquato Garulli ◽  
Anita Catapano ◽  
Daniele Fanteria ◽  
Julien Jumel ◽  
Eric Martin
Keyword(s):  
Finite Element ◽  
Crack Closure ◽  
Plate Theory ◽  
Closed Form Solution ◽  
Standard Test ◽  
Form Solution ◽  
Virtual Crack Closure Technique ◽  
Test Procedures ◽  
Closure Technique ◽  
Double Cantilever Beam Test

In this paper, a procedure to obtain fully uncoupled multi-directional stacking sequences for delamination specimens is outlined. For such sequences, in-plane, membrane-bending and torsion–bending coupling terms are null (in closed-form solution in the framework of classical laminated plate theory) for the entire stack and for both its halves, which form two arms in the pre-cracked region of a typical delamination specimen. This is achieved exploiting the superposition of quasi-trivial quasi-homogeneous stacking sequences, according to appropriate rules. Any pair of orientations of the plies embedding the delamination plane can be obtained. To assess the effectiveness of the proposed approach, a fully uncoupled multi-directional sequence is designed and compared to other relevant sequences proposed in the literature. Finite element simulations of double cantilever beam test are performed using classic virtual crack closure technique and a revised state-of-the-art virtual crack closure technique formulation too. Some interesting conclusions regarding proper design of multidirectional stacks for delamination tests are drawn. Moreover, the results confirm the suitability of fully uncoupled multi-directional sequences for delamination tests. Thanks to their properties, these sequences might lay the foundations for the development of standard test procedures for delamination in angle-ply interfaces.

A closed form solution for bending/stretching analysis of functionally graded circular plates under asymmetric loading using the Green function

2010 ◽  
Vol 224 (6) ◽  
pp. 1153-1163 ◽  
Author(s):  
A R Saidi ◽  
A Naderi ◽  
E Jomehzadeh
Keyword(s):  
Green Function ◽  
Closed Form ◽  
Volume Fraction ◽  
Plate Theory ◽  
Closed Form Solution ◽  
Form Solution ◽  
Functionally Graded ◽  
Transverse Displacement ◽  
Circular Plates ◽  
Equilibrium Equations

In this article, a closed-form solution for bending/stretching analysis of functionally graded (FG) circular plates under asymmetric loads is presented. It is assumed that the material properties of the FG plate are described by a power function of the thickness variable. The equilibrium equations are derived according to the classical plate theory using the principle of total potential energy. Two new functions are introduced to decouple the governing equilibrium equations. The three highly coupled partial differential equations are then converted into an independent equation in terms of transverse displacement. A closed-form solution for deflection of FG circular plates under arbitrary lateral eccentric concentrated force is obtained by defining a new coordinate system. This solution can be used as a Green function to obtain the closed-form solution of the FG plate under arbitrary loadings. Also, the solution is employed to solve some different asymmetric problems. Finally, the stress and displacement components are obtained exactly for each problem and the effect of volume fraction is also studied.

Closed-Form Representation of Beam Response to Moving Line Loads

2000 ◽  
Vol 68 (2) ◽  
pp. 348-350 ◽  
Author(s):  
Lu Sun
Keyword(s):  
Closed Form ◽  
Moving Load ◽  
Closed Form Solution ◽  
Form Solution ◽  
Winkler Foundation ◽  
Line Load ◽  
State Response ◽  
Form Representation ◽  
Mach Numbers ◽  
Moving Line

Fourier transform is used to solve the problem of steady-state response of a beam on an elastic Winkler foundation subject to a moving constant line load. Theorem of residue is employed to evaluate the convolution in terms of Green’s function. A closed-form solution is presented with respect to distinct Mach numbers. It is found that the response of the beam goes to unbounded as the load travels with the critical velocity. The maximal displacement response appears exactly under the moving load and travels at the same speed with the moving load in the case of Mach numbers being less than unity.

Local Reinforcement Effect of a Strain Gauge Installation on Low Modulus Materials

2005 ◽  
Vol 40 (7) ◽  
pp. 643-653 ◽  
Author(s):  
A Ajovalasit ◽  
B Zuccarello
Keyword(s):  
Strain Gauge ◽  
Infinite Plate ◽  
Closed Form Solution ◽  
Adhesive Layer ◽  
Form Solution ◽  
Reinforcement Effect ◽  
Interface Shear ◽  
Technical Literature ◽  
Experimental Proof ◽  
Low Modulus

The reinforcement effect of electrical resistance strain gauges is well documented in the technical literature. In this paper the local reinforcement effect in tension is studied by using a simple theoretical model by considering a strain gauge mounted on a semi-infinite plate having the same width of the strain gauge and subjected to a uniaxial tension load. Neglecting the effect of the adhesive layer and considering the interface shear stress as an exponential distribution, the proposed model gives a closed-form solution. In detail, this model permits a simple formula to be obtained which allows the user to correct the local reinforcement effect provided that a proper calibration is performed by installing a strain gauge, of the same type as that used on the structure, on a low modulus material. Experimental evidence of the proposed method is shown. Experimental proof of the positive effect of large grid lengths on the local reinforcement effect is also reported.

scholarly journals A Novel Higher-Order Shear and Normal Deformable Plate Theory for the Static, Free Vibration and Buckling Analysis of Functionally Graded Plates

2017 ◽  
Vol 2017 ◽  
pp. 1-20 ◽  
Author(s):  
Shi-Chao Yi ◽  
Lin-Quan Yao ◽  
Bai-Jian Tang
Keyword(s):  
Natural Frequencies ◽  
Plate Theory ◽  
Closed Form Solution ◽  
Higher Order ◽  
Form Solution ◽  
Functionally Graded ◽  
The Novel ◽  
Functionally Graded Plates ◽  
Graded Materials ◽  
Different Shapes

Closed-form solution of a special higher-order shear and normal deformable plate theory is presented for the static situations, natural frequencies, and buckling responses of simple supported functionally graded materials plates (FGMs). Distinguished from the usual theories, the uniqueness is the differentia of the new plate theory. Each individual FGM plate has special characteristics, such as material properties and length-thickness ratio. These distinctive attributes determine a set of orthogonal polynomials, and then the polynomials can form an exclusive plate theory. Thus, the novel plate theory has two merits: one is the orthogonality, where the majority of the coefficients of the equations derived from Hamilton’s principle are zero; the other is the flexibility, where the order of the plate theory can be arbitrarily set. Numerical examples with different shapes of plates are presented and the achieved results are compared with the reference solutions available in the literature. Several aspects of the model involving relevant parameters, length-to-thickness, stiffness ratios, and so forth affected by static and dynamic situations are elaborate analyzed in detail. As a consequence, the applicability and the effectiveness of the present method for accurately computing deflection, stresses, natural frequencies, and buckling response of various FGM plates are demonstrated.

The Axially Loaded Circular Cylinder

1962 ◽  
Vol 29 (2) ◽  
pp. 318-320
Author(s):  
H. D. Conway
Keyword(s):  
Exact Solution ◽  
Fourier Transform ◽  
Circular Cylinder ◽  
Closed Form ◽  
Cross Sections ◽  
Closed Form Solution ◽  
Form Solution ◽  
Concentrated Force ◽  
Transform Method ◽  
Fourier Transform Method

Commencing with Kelvin’s closed-form solution to the problem of a concentrated force acting at a given point in an indefinitely extended solid, a Fourier transform method is used to obtain an exact solution for the case when the force acts along the axis of a circular cylinder. Numerical values are obtained for the maximum direct stress on cross sections at various distances from the force. These are then compared with the corresponding stresses from the solution for an infinitely long strip, and in both cases it is observed that the stresses are practically uniform on cross sections greater than a diameter or width from the point of application of the load.

scholarly journals Dynamic Analysis of an Infinitely Long Beam Resting on a Kelvin Foundation under Moving Random Loads

2017 ◽  
Vol 2017 ◽  
pp. 1-13
Author(s):  
Y. Zhao ◽  
L. T. Si ◽  
H. Ouyang
Keyword(s):  
Fourier Transform ◽  
Random Vibration ◽  
Moving Load ◽  
Closed Form Solution ◽  
Form Solution ◽  
Integration Scheme ◽  
Random Loads ◽  
Numerical Integration Scheme ◽  
Vibration Responses ◽  
The Fourier Transform

Nonstationary random vibration analysis of an infinitely long beam resting on a Kelvin foundation subjected to moving random loads is studied in this paper. Based on the pseudo excitation method (PEM) combined with the Fourier transform (FT), a closed-form solution of the power spectral responses of the nonstationary random vibration of the system is derived in the frequency-wavenumber domain. On the numerical integration scheme a fast Fourier transform is developed for moving load problems through a parameter substitution, which is found to be superior to Simpson’s rule. The results obtained by using the PEM-FT method are verified using Monte Carlo method and good agreement between these two sets of results is achieved. Special attention is paid to investigation of the effects of the moving load velocity, a few key system parameters, and coherence of loads on the random vibration responses. The relationship between the critical speed and resonance is also explored.

Degenerate Scale Problem for a Hypocycloid Hole in an Infinite Plate in Plane Elasticity

2016 ◽  
Vol 32 (4) ◽  
pp. N7-N10
Author(s):  
Y.-Z. Chen
Keyword(s):  
Boundary Condition ◽  
Conformal Mapping ◽  
Closed Form ◽  
Infinite Plate ◽  
Closed Form Solution ◽  
Plane Elasticity ◽  
Form Solution ◽  
Scale Problem ◽  
Exterior Region ◽  
Degenerate Scale

AbstractBased on the conformal mapping, this paper provides a closed form solution for the degenerate scale of the hypocycloid hole in plane elasticity. In the derivation, we assume the vanishing displacements along the boundary in the degenerate scale problem. Some functions in the boundary condition are decomposed into three parts with particular behavior. Even the displacements are vanishing along the boundary of an exterior region, the displacements and stresses are not equal to zero in the exterior region. This is a particular feature in the degenerate scale problem.

Thermoelastic Fields in Boundary Layers of Isotropic Laminates

2005 ◽  
Vol 72 (1) ◽  
pp. 86-101 ◽  
Author(s):  
Christian Mittelstedt ◽  
Wilfried Becker
Keyword(s):  
Closed Form ◽  
Edge Effects ◽  
Plate Theory ◽  
Closed Form Solution ◽  
Laminate Plate ◽  
Free Edge ◽  
Linear Displacement ◽  
Form Solution ◽  
State Variables ◽  
Layered Plates

An approximate approach to the calculation of displacements, strains, and stresses near edges and corners in symmetric rectangular layered plates of dissimilar isotropic materials under thermal load is presented. In the thickness direction the plate is discretized into an arbitrary number of sublayers/mathematical layers. A layerwise linear displacement field is formulated such that the terms according to classical laminate plate theory are upgraded with unknown in-plane functions and a linear interpolation scheme through the layer thickness in order to describe edge and corner perturbations. By virtue of the principle of minimum potential energy the governing coupled Euler–Lagrange differential equations are derived, which in the case of free-edge effects allow a closed-form solution for the unknown inplane functions. Free-corner effects are investigated by combining the displacement formulations of the two interacting free-edge effects. Hence, all state variables in the plate are obtained in a closed-form manner. Boundary conditions of traction free plate edges are satisfied in an integral sense. The present methodology is easily applied and requires only reasonable computational expenses.

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