scholarly journals Use of Higher Order Plate Theory in dynamic analysis of SSFS and CSFS thick rectangular plates in orthogonal polynomials

2021 ◽  
Vol 40 (2) ◽  
pp. 199-209
Author(s):  
I.C. Onyechere ◽  
U.C. Anya ◽  
O.M. Ibearugbulem ◽  
A.U. Igbojiaku ◽  
E.O. Ihemegbulem ◽  
...  
Keyword(s):  
Potential Energy ◽  
Governing Equation ◽  
Plate Theory ◽  
Total Potential Energy ◽  
The Other ◽  
Frequency Function ◽  
Rectangular Plates ◽  
Total Potential ◽  
Edge Conditions ◽  
Simple Supports

This study applied polynomial expressions as displacement and shear deformation functions in the free-vibration study of thick and moderately thick isotropic rectangular plates. Rectangular plates with two different edge conditions investigated in this work are: one with simple supports at three of its edges and with no support at the other edge denoted with the acronym (SSFS) and a rectangular plate with simple supports at opposite edges while the other opposite edges has a fixed support at one edge and no support at the other edge, this is denoted with the acronym (CSFS). The total potential energy of the plate was derived using the general theory of elasticity. The general governing equation of the plate was derived by minimizing the total potential energy equation of the plate. Edge conditions of the SSFS and CSFS plates were met and substituted into the general governing equation to obtain a linear expression which was solved to generate fundamental natural frequency function for the plates with various span-depth proportion (m/t) and planar dimensions proportion (n/m). The results obtained from this research were found to agree favourably with the results of similar problems in the literature upon comparison.

scholarly journals Exact Three-Dimensional Stability Analysis of Plate Using an Direct Variational Energy Method

2022 ◽  
Vol 8 (1) ◽  
pp. 60-80
Author(s):  
F. C. Onyeka ◽  
B. O. Mama ◽  
T. E. Okeke
Keyword(s):  
Stability Analysis ◽  
Potential Energy ◽  
Governing Equation ◽  
Thick Plate ◽  
Constitutive Relations ◽  
Three Dimensional ◽  
Energy Functional ◽  
Total Potential Energy ◽  
Average Percentage ◽  
Total Potential

In this paper, direct variational calculus was put into practical use to analyses the three dimensional (3D) stability of rectangular thick plate which was simply supported at all the four edges (SSSS) under uniformly distributed compressive load. In the analysis, both trigonometric and polynomial displacement functions were used. This was done by formulating the equation of total potential energy for a thick plate using the 3D constitutive relations, from then on, the equation of compatibility was obtained to determine the relationship between the rotations and deflection. In the same way, governing equation was obtained through minimization of the total potential energy functional with respect to deflection. The solution of the governing equation is the function for deflection. Functions for rotations were obtained from deflection function using the solution of compatibility equations. These functions, deflection and rotations were substituted back into the energy functional, from where, through minimizations with respect to displacement coefficients, formulas for analysis were obtained. In the result, the critical buckling loads from the present study are higher than those of refined plate theories with 7.70%, signifying the coarseness of the refined plate theories. This amount of difference cannot be overlooked. However, it is shown that, all the recorded average percentage differences between trigonometric and polynomial approaches used in this work and those of 3D exact elasticity theory is lower than 1.0%, confirming the exactness of the present theory. Thus, the exact 3D plate theory obtained, provides a good solution for the stability analysis of plate and, can be recommended for analysis of any type of rectangular plates under the same loading and boundary condition. Doi: 10.28991/CEJ-2022-08-01-05 Full Text: PDF

A simplified formulation of adhesion problems with elastic plates

2009 ◽  
Vol 465 (2107) ◽  
pp. 2217-2230 ◽  
Author(s):  
Carmel Majidi ◽  
George G. Adams
Keyword(s):  
Potential Energy ◽  
Contact Area ◽  
Contact Region ◽  
Bending Moment ◽  
Total Potential Energy ◽  
Work Of Adhesion ◽  
Contact Radius ◽  
Algebraic Complexity ◽  
Elastic Plates ◽  
Total Potential

The solution of adhesion problems with elastic plates generally involves solving a boundary-value problem with an assumed contact area. The contact region is then found by minimizing the total potential energy with respect to the contact area (i.e. the contact radius for the axisymmetric case). Such a procedure can be extremely long and tedious. Here, we show that the inclusion of adhesion is equivalent to specifying a discontinuous internal bending moment at the contact region boundary. The magnitude of this moment discontinuity is related to the work of adhesion and flexural rigidity of the plate. Such a formulation can greatly reduce the algebraic complexity of solving these problems. It is noted that the related plate contact problems without adhesion can also be solved by minimizing the total potential energy. However, it has long been recognized that it is mathematically more efficient to find the contact area by specifying a continuous internal bending moment at the boundary of the contact region. Thus, our moment discontinuity method can be considered to be a generalization of that procedure which is applicable for problems with adhesion.

Some Thin-Plate Problems by the Sine Transform

1951 ◽  
Vol 18 (2) ◽  
pp. 152-156
Author(s):  
L. I. Deverall ◽  
C. J. Thorne
Keyword(s):  
Thin Plate ◽  
The Other ◽  
Rectangular Plates ◽  
Specific Load ◽  
General Solutions ◽  
Arbitrary Load ◽  
Sine Transform ◽  
Edge Conditions ◽  
Method Of Solution ◽  
Load Function

Abstract General expressions for the deflection of thin rectangular plates are obtained for cases in which two opposite edges have arbitrary but given deflections and moments. The sine transform is used as a part of the method of solution, since solutions can be found for an arbitrary load for each set of edge conditions at the other two edges. Even for the classical cases, the use of the sine transform makes the process of solving the problem much easier. The six general solutions given are those which arise from all possible combinations of physically important edge conditions at the other two edges. Solutions for a specific load function can be found by integration or by the use of a table of sine transforms. Tables useful in application of the method to specific problems are included.

An Optimization Method for the Static Balancing of Manipulators Using Springs

2020 ◽  
Author(s):  
Jieyu Wang ◽  
Xianwen Kong
Keyword(s):  
Potential Energy ◽  
Objective Function ◽  
Multiple Solutions ◽  
Optimization Method ◽  
Total Potential Energy ◽  
Static Balancing ◽  
Attachment Point ◽  
Total Potential

Abstract This paper discusses a novel optimization method to design statically balanced manipulators. Only springs are used to balance the manipulators composed of revolute (R) joints. Since the total potential energy of the system is constant when statically balanced, the sum of squared differences between the two potential energy when giving different random values of joint variables is set as the objective function. Then the optimization tool of MATLAB is used to obtain the spring attachment points. The results show that for a 1-link manipulator mounted on an R joint, in addition to attaching the spring right above the R joint, the attachment point can have offset. It also indicates that an arbitrary spatial manipulator with n link, whose weight cannot be neglected, can be balanced using n springs. Using this method, the static balancing can be readily achieved, with multiple solutions.

Automatic Refinement of FE Shell Models Based on a Local Energy Function

2013 ◽  
Author(s):  
Antonio Carminelli ◽  
Giuseppe Catania
Keyword(s):  
Potential Energy ◽  
Local Density ◽  
Free Vibration Analysis ◽  
Element Model ◽  
Companion Paper ◽  
Total Potential Energy ◽  
Shape Functions ◽  
Total Potential ◽  
Error Functional ◽  
Local Patch

This paper deals with an adaptive refinement technique of a B-spline degenerate shell finite element model, for the free vibration analysis of curved thin and moderately thick-walled structures. The automatic refinement of the solution is based on an error functional related to the density of the total potential energy. The model refinement is generated by locally increasing, in a sub-domain R of a local patch domain, the number of shape functions while maintaining constant the functions polynomial order. The local refinement strategy is described in a companion paper, written by the same authors of this paper and presented in this Conference. A two-step iterative procedure is proposed. In the first step, one or more sub domains to be refined are identified by means of a point-wise error functional based on the system total potential energy local density. In the second step, the number of shape functions to be added is iteratively increased until the difference of the total potential energy, calculated on the sub domain between two iteration, is below a user defined tolerance. A numerical example is presented in order to test the proposed approach. Strengths and limits of the approach are critically discussed.

First-Principles Study on Crystal Configuration and Many-Body Cohesive Energy of Solid Argon

2019 ◽  
Vol 807 ◽  
pp. 135-140
Author(s):  
Xi Jin Fu
Keyword(s):  
Potential Energy ◽  
Interaction Energy ◽  
First Principles ◽  
Total Potential Energy ◽  
Basis Set ◽  
Many Body ◽  
Body Interaction ◽  
Total Potential ◽  
Geometric Configurations ◽  
Solid Argon

Based on the first-principles, using CCSD(T) ab initio calculation method, many-body potential energy of solid argon are accurately calculated with the atomic distance R from 2.0Å to 3.6Å at T=300K, and firstly establish and discuss the face-centered cubic (fcc) atomic crystal configurations of two-, three-, and four-body terms by geometry optimization. The results shows that the total number of (Ar)2 clusters is 903, which belongs to 12 different geometric configurations, the total number of (Ar)3 clusters is 861, which belongs to 25 different geometric configurations, and the total number of (Ar)4 clusters of is 816 which belongs to 27 different geometric configurations. We find that the CCSD(T) with the aug-cc-pVQZ basis set is most accurate and practical by comprehensive consideration. The total potential energy Un reachs saturation at R>2.0Å when the only two-and three-body interaction energy are considered. When R≤2.0Å, the total potential energy Un must consider four-and higher-body interaction energy to achieve saturation. Many-body expansion potential of fcc solid argon is an exchange convergent series.

Energy-free adjustment of gravity equilibrators by adjusting the spring stiffness

2008 ◽  
Vol 222 (9) ◽  
pp. 1839-1846 ◽  
Author(s):  
W D van Dorsser ◽  
R Barents ◽  
B M Wisse ◽  
M Schenk ◽  
J L Herder
Keyword(s):  
Potential Energy ◽  
Total Potential Energy ◽  
Spring Stiffness ◽  
External Energy ◽  
Static Balancing ◽  
Concept Model ◽  
Total Potential ◽  
Novel Variant ◽  
Energy Conserving

Static balancing is a useful concept to reduce the operating effort of mechanisms. Spring mechanisms are used to achieve a constant total potential energy, thus eliminating any preferred position. Quasi-statically, the mechanism, once statically balanced, can be moved virtually without the operating energy. In some cases, it is desirable to adjust the characteristic of the balancer, for instance, due to a change in the payload in a gravity balanced mechanism. The adjustment of current static balancers requires significant operating energy. This paper will present a novel variant to adjust the spring- and linkage-based static balancers without the need for external energy. The variant makes use of the possibility to adjust the spring stiffness in an energy-conserving way by adjusting the number of active coils. The conditions under which it functions properly will be given, and a proof of the concept model will be shown.

Structure électronique de dérivés sulfures. XI. Thiétanne et dérivés

1975 ◽  
Vol 53 (8) ◽  
pp. 1224-1236 ◽  
Author(s):  
Claude Guimon ◽  
Daniel Liotard ◽  
Geneviève Pfister-Guillouzo
Keyword(s):  
Experimental Data ◽  
Potential Energy ◽  
Total Potential Energy ◽  
Geometric Parameters ◽  
The Third ◽  
Total Potential ◽  
Partial Energy ◽  
Chloro Derivatives ◽  
Semi Empirical ◽  
Structure Electronique

The conformations of thietane, thietane sulfoxide, and their 3-chloro derivatives were obtained theoretically by minimization of the energy with respect to geometric parameters using the semi-empirical CNDO/2 method extended to the third period. The results agree well with known experimental data. The respective stabilities of the different conformers are explained by partial energy results obtained by a bicentric partition of the total potential energy of the molecules. [Journal translation]

Bending of Sandwich Plates of Variable Thickness

1988 ◽  
Vol 55 (2) ◽  
pp. 419-424 ◽  
Author(s):  
N. Paydar ◽  
C. Libove
Keyword(s):  
Potential Energy ◽  
Variable Thickness ◽  
Middle Surface ◽  
Total Potential Energy ◽  
Sandwich Plates ◽  
Energy Principle ◽  
Total Potential ◽  
Small Deflection ◽  
The Face ◽  
Deflection Theory

A small deflection theory, consisting of differential equations and a total potential energy expression, is presented for determining the stresses and deformations in variable thickness elastic sandwich plates symmetric about a middle surface. The theory takes into account the contribution of the face-sheet membrane forces (by virtue of their slopes) to the transverse shear. A finite-difference formulation of the stationary total potential energy principle is presented along with an illustrative application.

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