Solution of Rectangular Clamped Plate With Lateral Load by Generalized Energy Method

1939 ◽  
Vol 6 (4) ◽  
pp. A168-A170
Author(s):  
Gerald Pickett
Keyword(s):  
Rectangular Plate ◽  
Energy Method ◽  
Lateral Load ◽  
Clamped Plate

Abstract The author gives formulas by which the energy method may be readily applied for obtaining the moments and deflections for any lateral load on a clamped rectangular plate. He not only gives mathematical computations illustrating the application of the formulas, but also discusses the accuracy of the method compared to others, and points out its limitations.

Large Deflection of a Rectangular Plate Resting on a Pasternak-Type Elastic Foundation

1977 ◽  
Vol 44 (3) ◽  
pp. 509-511 ◽  
Author(s):  
P. K. Ghosh
Keyword(s):  
Rectangular Plate ◽  
Elastic Foundation ◽  
Large Deflection ◽  
Lateral Load ◽  
Bending Moments ◽  
Shear Forces ◽  
Simply Supported ◽  
Base Parameters ◽  
Square Plate

The problem of large deflection of a rectangular plate resting on a Pasternak-type foundation and subjected to a uniform lateral load has been investigated by utilizing the linearized equation of plates due to H. M. Berger. The solutions derived and based on the effect of the two base parameters have been carried to practical conclusions by presenting graphs for bending moments and shear forces for a square plate with all edges simply supported.

The effect of two isolated forces on the elastic stability of a flat rectangular plate

1937 ◽  
Vol 33 (3) ◽  
pp. 325-339 ◽  
Author(s):  
D. M. A. Leggett
Keyword(s):  
Rectangular Plate ◽  
Energy Method ◽  
Strain Energy ◽  
Close Agreement ◽  
Elastic Stability ◽  
Underlying Assumption ◽  
Simply Supported ◽  
The Common ◽  
External Forces ◽  
Strain Energy Method

1. Introduction and summary. The problem of the elastic stability of a simply supported rectangular plate, compressed by two equal and opposite forces acting in the plane of the plate (see Fig. 1), was first attempted by A. Sommerfeld, and later by S. Timoshenko. The former produced a solution which in a later paper he admitted to be liable to very considerable error, while the latter constructed a solution by means of the well-known strain-energy method. In many problems this method gives results in very close agreement with those obtained in a more rigorous manner, but, in the particular case considered here, it appeared likely that the error would be appreciable owing to the underlying assumption that the only stresses in the plate occurred along the common line of action of the two external forces.

scholarly journals CRITICAL LATERAL LOAD ANALYSIS OF RECTANGULAR PLATE CONSIDERING SHEAR DEFORMATION EFFECT

2020 ◽  
pp. 16-27
Author(s):  
F. C. Onyeka
Keyword(s):  
Potential Energy ◽  
Shear Deformation ◽  
Rectangular Plate ◽  
Thick Plate ◽  
Shear Deformation Theory ◽  
Lateral Load ◽  
Width Ratio ◽  
Total Potential ◽  
Transverse Loads ◽  
Total Failure

This work present flexural analysis of rectangular plate subjected to uniform distributed transverse loads using displacement and third-order shear deformation theory. The aim of this study is to establish the formula’s for calculation of the critical lateral imposed load of the plate before deflection reaches the specified maximum specified limit q𝑖𝑤 and critical lateral imposed load before plate reaches an elastic yield point q𝑖𝑝. The essence is to ensure that deflection does not exceed specified maximum limit and the plate shear not exceeding the elastic yielding point. Furthermore, this approach overcomes the challenges of the conventional practice in the structural analysis/design which involves checking of deflection and shear; the process which is proved unreliable. Total potential energy equation of a thick plate was formulated from the static elastic theory of the plate. The formulated potential energy was in the same way used by the method of direct variation to obtain the coefficient of deflection and shear deformation. This expression was applied to solve bending problem of two different types of rectangular thick plates. The plates has one edge clamped and other three edges simply supported (CSSS). From the result obtained in this work among the two types of plate, it is observed that the value of q𝑖𝑝 if greater than that of q𝑖𝑤. It can be said that the failure of plate in q𝑖𝑤 is like a warning requesting maintenance whereas failure in q𝑖𝑝 means total failure and cannot be maintained. Hence, failure in deflection (q𝑖𝑤) is seen in the plate into consideration. The numerical analysis obtained, it is found that if the value of critical lateral imposed load (q𝑖𝑤 and q𝑖𝑝) increase as the specified thickness (t) of plate increases and decrease as the length to width ratio increases. This implies that as we increase the thickness and allowable deflection improve the safety in the plate, whereas an increase in the span (length) of the plate increases the failure tendency of the plate structure. Furthermore, effects of aspect ratio of the critical lateral load of isotropic plates are investigated and discussed. It is concluded that the values of critical lateral load obtained by this theory achieve accepted transverse shear stress to the thickness of plate variation and satisfied the transverse flexibility of the condition of the plate while predicting the be characteristics for the CSSS isotropic rectangular thin or thick plate.

The Effect of Welding Self-Equilibrating Stresses on the Natural Frequencies of Thin Rectangular Plate With Edges Rotational Flexibility

2005 ◽  
Author(s):  
Albert E. Yousif ◽  
Shakir Al-Samarrai ◽  
A. Salam Al-Ammri
Keyword(s):  
Residual Stresses ◽  
Rectangular Plate ◽  
Energy Method ◽  
Natural Frequencies ◽  
Vibration Characteristics ◽  
Thin Rectangular Plate ◽  
Special Solutions ◽  
General Frequency ◽  
Elastically Restrained ◽  
Good Agreement

An investigation has been made into the effect of residual stresses on the vibration characteristics of a thin rectangular plate elastically restrained against rotation along all edges using an energy method. General frequency equations with and without the effect of residual stresses have been obtained. Exact frequency equations with and without the effect of residual stresses for the cases: C-C-C-C, S-S-S-S, S-S-C-S, C-S-C-S, S-S-C-C, C-C-C-S have also been obtained. Exact equations were derived including the effect of the position of welding along the width of the plate for all cases considered. The validity of the equations obtained was checked with available special solutions with a good agreement.

The Elastically Clamped Rectangular Plate With Arbitrary Lateral and Thermal Loading

1962 ◽  
Vol 29 (3) ◽  
pp. 578-580
Author(s):  
C. C. Chao ◽  
Max Anuliker
Keyword(s):  
Rectangular Plate ◽  
Thin Plate ◽  
Infinite Series ◽  
Series Solution ◽  
Thermal Loading ◽  
Plate Theory ◽  
Convergent Series ◽  
Clamped Plate ◽  
Simply Supported ◽  
Thin Plate Theory

Within the limits of classical thin-plate theory a variety of elementary problems have been solved for the rectangular plate3,4,5. In particular, the rectangular plate with edges simply supported or clamped has been dealt with at length and the solution to different loading cases given either in the form of a doubly infinite series or a single infinite series. In this paper a rapidly convergent series solution is outlined for the uniformly elastically clamped plate which is subjected to nonuniform lateral and thermal loading. The solution converges in the limit to those corresponding to the simply supported and rigidly clamped plate.

scholarly journals On the Solution to Pre- Buckling of a Thin Rectangular Plate Subjected to a Thick Strip in-plane Loading

2021 ◽  
Vol 16 ◽  
pp. 198-205
Author(s):  
Jacob Nagler
Keyword(s):  
Rectangular Plate ◽  
Energy Method ◽  
Strain Energy ◽  
Euler Method ◽  
General View ◽  
Thin Rectangular Plate ◽  
Transverse Loads ◽  
Buckling Stress ◽  
Strain Energy Method ◽  
Plate Width

The current paper deals with the problem of the simply supported thin rectangular plate subjected to the intermediate strip in-plane loading. Based on the strain energy method (Fourier ansatz), the critical (minimum value) of buckling stress occurrence was determined in a general form dependent only on the strip thickness, strip location, plate width and stress magnitude. Compatible with the classical columns Euler method it was found that the plate stability is decreased with the increasing of the plate width due to larger induced stresses. Also, strip location relative to the support region was found to influence the buckling (same analogy to the Euler buckling theory; consider the strip as a both sides pressed rod). Additionally, the strip width parameter increase is likely to cause larger buckling stress. Moreover, expressions that includes both axial and transverse loads for different extended cases configurations were also derived and examined based on the strain energy method alongside explanation for possible applications (thin aluminum plate welding). In a general view, it was found that the cases of combined axial and perpendicular loading action are less stabilized than cases where only one kind of loading configuration is participated. Finally, the buckling stress was found to agree qualitatively with the cited literature.

Sign in / Sign up

Export Citation Format

Share Document