Closed-Form Solutions for Eigenbuckling of Rectangular Mindlin Plate

2016 ◽  
Vol 16 (08) ◽  
pp. 1550079 ◽  
Author(s):  
Yufeng Xing ◽  
Wei Xiang
Keyword(s):  
Closed Form ◽  
Present Method ◽  
Separation Of Variables ◽  
Mindlin Plate ◽  
Rectangular Plates ◽  
Closed Form Solutions ◽  
Simply Supported ◽  
Major Development ◽  
First Time ◽  
Good Agreement

This paper studies the eigenbuckling of Mindlin plate with two adjacent edges clamped and the remaining edges simply supported or clamped by using the separation of variables method, and the concise and explicit closed-form solutions are obtained for the first time. The cases involving free edges can also be dealt with if there are two opposite edges simply supported. The closed-form solutions are in good agreement with the existing solutions, thus the validity of present method and accuracy of the obtained solutions are verified. This paper proves to be a major development of analytical method since it has long been acknowledged that the eigenbuckling of rectangular plates without two parallel edges simply supported are not amenable to analytical solutions.

scholarly journals Delay chemical master equation: direct and closed-form solutions

2015 ◽  
Vol 471 (2179) ◽  
pp. 20150049 ◽  
Author(s):  
Andre Leier ◽  
Tatiana T. Marquez-Lago
Keyword(s):  
Master Equation ◽  
Closed Form ◽  
Stochastic Simulation Algorithm ◽  
Chemical Master Equation ◽  
Kolmogorov Equation ◽  
Closed Form Solutions ◽  
Mrna Maturation ◽  
First Time ◽  
Nonlinear Markov Process ◽  
Reaction Schemes

The stochastic simulation algorithm (SSA) describes the time evolution of a discrete nonlinear Markov process. This stochastic process has a probability density function that is the solution of a differential equation, commonly known as the chemical master equation (CME) or forward-Kolmogorov equation. In the same way that the CME gives rise to the SSA, and trajectories of the latter are exact with respect to the former, trajectories obtained from a delay SSA are exact representations of the underlying delay CME (DCME). However, in contrast to the CME, no closed-form solutions have so far been derived for any kind of DCME. In this paper, we describe for the first time direct and closed solutions of the DCME for simple reaction schemes, such as a single-delayed unimolecular reaction as well as chemical reactions for transcription and translation with delayed mRNA maturation. We also discuss the conditions that have to be met such that such solutions can be derived.

Application of large-deflection theory to normally loaded rectangular plates with clamped edges

1970 ◽  
Vol 5 (2) ◽  
pp. 140-144 ◽  
Author(s):  
A Scholes
Keyword(s):  
Large Deflection ◽  
Rectangular Plates ◽  
Simply Supported ◽  
Aspect Ratios ◽  
Non Linear ◽  
Deflection Theory ◽  
Large Deflection Theory ◽  
Clamped Edges ◽  
Clamped Edge ◽  
Good Agreement

A previous paper (1)∗described an analysis for plates that made use of non-linear large-deflection theory. The results of the analysis were compared with measurements of deflections and stresses in simply supported rectangular plates. In this paper the analysis has been used to calculate the stresses and deflections for clamped-edge plates and these have been compared with measurements made on plates of various aspect ratios. Good agreement has been obtained for the maximum values of these stresses and deflections. These maximum values have been plotted in such a form as to be easily usable by the designer of pressure-loaded clamped-edge rectangular plates.

Thermal Bending of Thick Rectangular Plates of Bimodulus Composite Materials

1980 ◽  
Vol 22 (6) ◽  
pp. 297-304 ◽  
Author(s):  
J. N. Reddy ◽  
C. W. Ber ◽  
Y. S. Hsu ◽  
V. S. Reddy
Keyword(s):  
Finite Element ◽  
Closed Form ◽  
Plate Theory ◽  
Laminated Composite ◽  
Composite Plates ◽  
Normal Strain ◽  
Rectangular Plates ◽  
Fibre Direction ◽  
Thermal Bending ◽  
Good Agreement

Closed-form and finite-element solutions are presented for thermal bending and stretching of laminated composite plates. The material of each layer is assumed to be elastically and thermoelastically orthotropic and bimodular, i.e., having different properties depending upon whether the fibre-direction normal strain is tensile or compressive. The formulations are based on the thermoelastic version of the Whitney-Pagano laminated plate theory, which includes thickness shear deformations. Numerical results are obtained for deflections and neutral-surface positions associated with normal strains in both of the in-plane coordinates. The closed-form and finite-element results are found to be in good agreement.

KINEMATIC ANALYSIS AND PROTOTYPE OF A METAMORPHIC ANTHROPOMORPHIC HAND WITH A RECONFIGURABLE PALM

2011 ◽  
Vol 08 (03) ◽  
pp. 459-479 ◽  
Author(s):  
GUOWU WEI ◽  
JIAN S. DAI ◽  
SHUXIN WANG ◽  
HAIFENG LUO
Keyword(s):  
Closed Form ◽  
Matrix Equation ◽  
Kinematic Analysis ◽  
Structure Design ◽  
Characteristic Matrix ◽  
Robotic Hand ◽  
Closed Form Solutions ◽  
First Time

A novel metamorphic anthropomorphic hand is for the first time introduced in this paper. This robotic hand has a reconfigurable palm that generates changeable topology and augments dexterity and versatility of the hand. Structure design of the robotic hand is presented and based on mechanism decomposition kinematics of the metamorphic anthropomorphic hand is characterized with closed-form solutions leading to the workspace investigation of the robotic hand. With characteristic matrix equation, twisting motion of the metamorphic robotic hand is investigated to reveal both dexterity and manipulability of the metamorphic hand. Through a prototype, grasping and prehension of the robotic hand are tested to illustrate characteristics of the new metamorphic anthropomorphic hand.

Dynamic Response of a Timoshenko Beam to a Moving Force

2008 ◽  
Vol 75 (2) ◽  
Author(s):  
Paweł Śniady
Keyword(s):  
Closed Form ◽  
Cross Section ◽  
Timoshenko Beam ◽  
Constant Velocity ◽  
Free Vibrations ◽  
Dynamical Response ◽  
Transverse Displacement ◽  
Closed Form Solutions ◽  
Simply Supported ◽  
Moving Force

We consider the dynamical response of a finite, simply supported Timoshenko beam loaded by a force moving with a constant velocity. The classical solution for the transverse displacement and the rotation of the cross section of a Timoshenko beam has a form of a sum of two infinite series, one of which represents the force vibrations (aperiodic vibrations) and the other one free vibrations of the beam. We show that one of the series, which represents aperiodic (force) vibrations of the beam, can be presented in a closed form. The closed form solutions take different forms depending if the velocity of the moving force is smaller or larger than the velocities of certain shear and bar velocities.

Apparently First Closed-Form Solution for Frequencies of Deterministically and/or Stochastically Inhomogeneous Simply Supported Beams

2000 ◽  
Vol 68 (2) ◽  
pp. 176-185 ◽  
Author(s):  
S. Candan ◽  
I. Elishakoff
Keyword(s):  
Closed Form ◽  
Infinite Number ◽  
Natural Frequencies ◽  
Closed Form Solution ◽  
Form Solution ◽  
Numerical Examples ◽  
Closed Form Solutions ◽  
Simply Supported ◽  
Benchmark Solutions

An infinite number of closed-form solutions is reported for a deterministically or stochastically nonhomogeneous beam, for both natural frequencies and reliabilities, for specialized cases. These solutions may prove useful as benchmark solutions. Numerical examples are evaluated.

Improving Elmore Model of RLC Networks for Applying to SWCNT Interconnects

2011 ◽  
Vol 110-116 ◽  
pp. 5078-5084
Author(s):  
Behrouz Behtoee ◽  
Rahim Faez
Keyword(s):  
Carbon Nanotube ◽  
Closed Form ◽  
Curve Fitting ◽  
Rise Time ◽  
Step Response ◽  
Analytical Estimate ◽  
Single Wall Carbon ◽  
Closed Form Solutions ◽  
Improved Accuracy ◽  
First Time

Elmore delay has been widely used as an analytical estimate of the interconnect delays in the performance-driven synthesis and layout of VLSI routing topologies. In this paper, Closed-form solutions for the 50% delay, rise time and overshoots of the step response of distributed Single Wall Carbon Nanotube (SWCNT), which consists RC and RLC parts, are presented for the first time. The proposed approach retains both efficiency and simplicity of the equivalent Elmore model with significantly improved accuracy, through surface fitting (3D) instead of curve fitting (2D).

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