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.

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.

The Behaviour of Multiple Loops in Torsion

1988 ◽  
Vol 15 (3) ◽  
pp. 149-156 ◽  
Author(s):  
R. A. Cavina ◽  
N. E. Waters
Keyword(s):  
Energy Method ◽  
Strain Energy ◽  
Vertical Axis ◽  
Experimental Measurements ◽  
Complementary Strain ◽  
Radial Axis ◽  
Strain Energy Method ◽  
Good Agreement

The angular stiffness of a multiple looped span, subject to rotation about a vertical axis (torsion) and also to rotation about a horizontal or radial axis (mesio-distal tilt), have been derived using the complementary (strain) energy method. Experimental measurements on enlarged models were in good agreement with the values calculated from the theoretical relationships obtained. The variations in angular stiffness resulting from changes in the loop height, width, and position of clinical sized loops are discussed.

Infrastructure Sustainability

2011 ◽  
pp. 186-201
Author(s):  
Hoi Wai Shih ◽  
David Thambiratnam ◽  
Tommy Chan
Keyword(s):  
Energy Method ◽  
Strain Energy ◽  
Health State ◽  
Modal Strain Energy ◽  
Structural Health ◽  
Modal Strain Energy Method ◽  
Modal Flexibility ◽  
Before And After ◽  
Composite Bridges ◽  
Strain Energy Method

Assessing the structural health state of urban infrastructure is crucial in terms of infrastructure sustainability. This chapter uses dynamic computer simulation techniques to apply a procedure using vibration-based methods for damage assessment in multiple-girder composite bridges. In addition to changes in natural frequencies, this multi-criteria procedure incorporates two methods, namely, the modal flexibility and the modal strain energy method. Using the numerically simulated modal data obtained through finite element analysis software, algorithms based on modal flexibility and modal strain energy change, before and after damage, are obtained and used as the indices for the assessment of structural health state. The feasibility and capability of the approach is demonstrated through numerical studies of a proposed structure with six damage scenarios. It is concluded that the modal strain energy method is capable of application to multiple-girder composite bridges, as evidenced through the example treated in this chapter.

Determination of Longwall Mining-Induced Stress Using the Strain Energy Method

2015 ◽  
Vol 48 (6) ◽  
pp. 2421-2433 ◽  
Author(s):  
Mohammad Rezaei ◽  
Mohammad Farouq Hossaini ◽  
Abbas Majdi
Keyword(s):  
Energy Method ◽  
Strain Energy ◽  
Longwall Mining ◽  
Induced Stress ◽  
Strain Energy Method
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