DYNAMIC INSTABILITY OF COMPOSITE SKEW PLATES USING BOUNDARY CHARACTERISTIC ORTHOGONAL POLYNOMIALS

2014 ◽  
Vol 06 (06) ◽  
pp. 1450078 ◽  
Author(s):  
ABHINAV KUMAR ◽  
S. K. PANDA ◽  
RAJESH KUMAR
Keyword(s):  
Potential Energy ◽  
Boundary Conditions ◽  
Total Energy ◽  
Shear Deformation ◽  
Dynamic Instability ◽  
Energy Functional ◽  
Total Potential Energy ◽  
Bending Energy ◽  
Total Potential ◽  
Skew Plate

Dynamic instability analysis of laminated composite skew plate for different skew angles subjected to different type of linearly varying in-plane loadings is investigated. The analysis also includes the instability of skew plate under uniform bi-axial in-plane loading. The skew plate structural model is based on higher order shear deformation theory (HSDT), which accurately predicts the numerical results for thick skew plate. The total energy functional is derived for the skew plates from total potential energy and kinetic energy of the plate. The strain energy which is the part of total potential energy contains membrane energy, bending energy, additional bending energy due to additional change in curvature and shear energy due to shear deformation, respectively. The total energy functional is mapped into a square plate over which a set of orthonormal polynomials satisfying the essential boundary conditions is generated by Gram–Schmidt orthogonalization process. Different boundary conditions of skew plate have been correctly incorporated by using Rayleigh–Ritz method in conjunction with Boundary Characteristics Orthonormal Polynomials (BCOPs). The boundaries of dynamic instability regions are traced by the periodic solution of governing differential equations (Mathieu type equations) with period T and 2T. The width of instability region for uniform loading is higher than various types of linearly varying loadings (keeping the same peak intensity). Effect of various parameters like skew angle, aspect ratio, span-to-thickness ratio, boundary conditions and static load factor on dynamic instability has been investigated.

scholarly journals Atmospheric Available Energy

2012 ◽  
Vol 69 (12) ◽  
pp. 3745-3762 ◽  
Author(s):  
Peter R. Bannon
Keyword(s):  
Kinetic Energy ◽  
Potential Energy ◽  
Total Energy ◽  
General Circulation ◽  
Total Potential Energy ◽  
Maximum Amount ◽  
Hydrostatic Equilibrium ◽  
Gibbs Function ◽  
Available Energy ◽  
Total Potential

Abstract The total potential energy of the atmosphere is the sum of its internal and gravitational energies. The portion of this total energy available to be converted into kinetic energy is determined relative to an isothermal, hydrostatic, equilibrium atmosphere that is convectively and dynamically “dead.” The temperature of this equilibrium state is determined by minimization of a generalized Gibbs function defined between the atmosphere and its equilibrium. Thus, this function represents the maximum amount of total energy that can be converted into kinetic energy and, hence, the available energy of the atmosphere. This general approach includes the effects of terrain, moisture, and hydrometeors. Applications are presented for both individual soundings and idealized baroclinic zones. An algorithm partitions the available energy into available baroclinic and available convective energies. Estimates of the available energetics of the general circulation suggest that atmospheric motions are primarily driven by moist and dry fluxes of exergy from the earth’s surface with an efficiency of about two-thirds.

Analysis of Orthotropic Thin Rectangular Simply Supported Plate Subjected to both In-Plane Compression and Lateral Loads

2020 ◽  
Vol 48 ◽  
pp. 63-77
Author(s):  
D.O. Onwuka ◽  
O.M. Ibearugbulem ◽  
Duke Bertram
Keyword(s):  
Yield Strength ◽  
Potential Energy ◽  
Elastic Stability ◽  
Lateral Load ◽  
Energy Functional ◽  
Total Potential Energy ◽  
Lateral Loads ◽  
Total Potential ◽  
Plane Compression ◽  
Potential Energy Functional

This study presents the analysis of thin rectangular orthotropic plate, simply supported at all edges (SSSS) subjected to both in-plane compression and lateral loads. The total potential energy functional was used in the analysis. The general variation of the total potential energy functional was done and the governing equation was obtained. The solution of the direct integration of the governing equation gave the deflection of the plate as a product of the coefficient of deflection and an orthogonal polynomial shape function. The expression for the coefficient of deflection was obtained by the direct variation of the total potential energy functional. This was used to derive the equation for the Lateral load parameter of an orthotropic thin rectangular plate carrying both in-plane compression and lateral loads based on the maximum deflection condition and also based on the elastic stability (yield strength) condition. The peculiar deflection equation for the SSSS plate was obtained using the formulated polynomial shape function. Numerical examples were carried out to determine the lateral load parameters corresponding to various plate thickness and permissible deflection for orthotropic thin SSSS plate carrying both in-plane compression and lateral load. In the same way, the lateral load parameters using the elastic stability condition (yield strength) were obtained for yield strength of 275 MPa, 355 MPa and 410 MPa

scholarly journals Vibration and Buckling of Skew Plates Under Linearly Varying Edge Compression

2019 ◽  
Vol 24 (2) ◽  
pp. 271-283
Author(s):  
Abhinav Kumar ◽  
Sarat Kumar Panda ◽  
Sekhar Chandra Dutta
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Total Energy ◽  
Energy Functional ◽  
Buckling Load ◽  
Static Case ◽  
Critical Buckling Load ◽  
Orthonormal Polynomials ◽  
Skew Plate ◽  
Eigen Value

Pre-buckling vibration and buckling behaviour of composite skew plates subjected to linearly varying in-plane edge loading with different boundary conditions are studied. The total energy functional of the skew plate mapped from physical domain to computational domain over which a set of orthonormal polynomials satisfying the essential boundary conditions is generated by Gram-Schmidt orthogonalization process. Using Rayleigh-Ritz method in conjunction with Boundary Characteristics Orthonormal Polynomials, the total energy functional is converted into sets of algebraic equations for static stability problems and ordinary differential equation for free vibration problem. Pre-buckling vibration frequencies of the stressed skew plate are obtained by solving associated linear eigen value problem for free vibration and solution of the eigen value problem for static case results critical buckling load. From different parametric study, it is observed that the pre-buckling vibration frequency and critical buckling load increase with the increase of skew angle and edge restraint.

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.

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.

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