Sinusoidal Torsional Buckling of Bars of Angle Section Under Bending Loads, as a Problem in Plate Theory

1951 ◽  
Vol 18 (3) ◽  
pp. 285-292
Author(s):  
H. J. Plass
Keyword(s):  
Infinite Series ◽  
Plate Theory ◽  
Ritz Method ◽  
Compressive Load ◽  
Series Solutions ◽  
Torsional Buckling ◽  
Bending Load ◽  
Angle Section ◽  
Bending Loads

Abstract Timoshenko has applied plate theory to each leg of an angle-section bar to determine the critical compressive load needed to cause sinusoidal torsional buckling. In this paper his idea is used to calculate the critical bending load needed to cause sinusoidal torsional buckling of an angle bar. The bending is assumed to be applied so that the extreme fibers of the angle are in compression, the vertex in tension. Approximate results are first obtained by means of the Rayleigh-Ritz method. The approximate deflection functions from which the energy terms are computed are based upon certain infinite-series solutions. After having obtained approximate results, exact values are obtained, using the approximate values as a guide to limit the amount of calculation. The results of this calculation are shown in Fig. 5, where they are compared with those predicted by bar theory. Differences between the two theories become more noticeable as the bar becomes short compared to its flange width. It is found that the critical bending load becomes larger very rapidly as the ratio of length to width of the flanges decreases. Bar theory predicts no such increase. The reason for this difference is explained.

Nondestructive Measurement of In-Plane Residual Stress in Silicon Strips

1999 ◽  
Vol 591 ◽  
Author(s):  
Tieyu Zheng ◽  
Steven Danyluk
Keyword(s):  
Residual Stress ◽  
Residual Stresses ◽  
Large Deflection ◽  
Thin Plates ◽  
Nondestructive Measurement ◽  
Three Point Bending ◽  
Phase Stepping ◽  
Bending Load ◽  
Bending Loads ◽  
Processing Techniques

ABSTRACTThis paper reports the development of a shadow moiré technique to measure the in-plane residual stresses of thin, flat strips. This is an extension of prior work on the measurement of in-plane residual stresses in silicon plates and wafers. Phase stepping shadow moir6 and digital image processing techniques are employed to measure the deflections of the silicon plate specimens subjected to three-point-bending at several different loads. The measured deflections over the area of the silicon plates are fitted with an equation represented by a 2-D polynomial. With the theory of thin plates with large deflection, the fitting coefficients are used to extract the in-plane stresses at the different bending load. The residual stress is resolved by linear regression of the in-plane stresses versus bending loads.

scholarly journals Parametric structural modelling of fish bone active camber morphing aerofoils

2018 ◽  
Vol 29 (9) ◽  
pp. 2008-2026 ◽  
Author(s):  
Andres E Rivero ◽  
Paul M Weaver ◽  
Jonathan E Cooper ◽  
Benjamin KS Woods
Keyword(s):  
Analytical Model ◽  
Composite Laminates ◽  
Plate Theory ◽  
Ritz Method ◽  
Linear Equations ◽  
Variable Stiffness ◽  
Automated Analysis ◽  
Fish Bone ◽  
Two Dimensional ◽  
Wide Range

Camber morphing aerofoils have the potential to significantly improve the efficiency of fixed and rotary wing aircraft by providing significant lift control authority to a wing, at a lower drag penalty than traditional plain flaps. A rapid, mesh-independent and two-dimensional analytical model of the fish bone active camber concept is presented. Existing structural models of this concept are one-dimensional and isotropic and therefore unable to capture either material anisotropy or spanwise variations in loading/deformation. The proposed model addresses these shortcomings by being able to analyse composite laminates and solve for static two-dimensional displacement fields. Kirchhoff–Love plate theory, along with the Rayleigh–Ritz method, are used to capture the complex and variable stiffness nature of the fish bone active camber concept in a single system of linear equations. Results show errors between 0.5% and 8% for static deflections under representative uniform pressure loadings and applied actuation moments (except when transverse shear exists), compared to finite element method. The robustness, mesh-independence and analytical nature of this model, combined with a modular, parameter-driven geometry definition, facilitate a fast and automated analysis of a wide range of fish bone active camber concept configurations. This analytical model is therefore a powerful tool for use in trade studies, fluid–structure interaction and design optimisation.

Post-Buckling Failure Modes of X65 Steel Pipe: An Experimental and Numerical Study

2018 ◽  
Vol 140 (5) ◽  
Author(s):  
Nima Mohajer Rahbari ◽  
Mengying Xia ◽  
Xiaoben Liu ◽  
J. J. Roger Cheng ◽  
Millan Sen ◽  
...  
Keyword(s):  
Internal Pressure ◽  
Cross Section ◽  
Failure Modes ◽  
Bending Test ◽  
Bending Load ◽  
Post Buckling ◽  
X65 Steel ◽  
Bending Loads ◽  
Buckling Failure ◽  
Longitudinal Strains

In service pipelines exhibit bending loads in a variety of in-field situation. These bending loads can induce large longitudinal strains, which may trigger local buckling on the pipe's compressive side and/or lead to rupture of the pipe's tensile side. In this article, the post-buckling failure modes of pressurized X65 steel pipelines under monotonic bending loading conditions are studied via both experimental and numerical investigations. Through the performed full-scale bending test, it is shown that the post-buckling rupture is only plausible to occur in the pipe wall on the tensile side of the wrinkled cross section under the increased bending. Based on the experimental results, a finite element (FE)-based numerical model with a calibrated cumulative fracture criterion was proposed to conduct a parametric analysis on the effects of the internal pressure on the pipe's failure modes. The results show that the internal pressure is the most crucial variable that controls the ultimate failure mode of a wrinkled pipeline under monotonic bending load. And the post-buckling rupture of the tensile wall can only be reached in highly pressurized pipes (hoop stress no less than 70% SMYS for the investigated X65 pipe). That is, no postwrinkling rupture is likely to happen below a certain critical internal pressure even after an abrupt distortion of the wrinkled wall on the compressive side of the cross section.

Effects of In-plane Load on Flutter of Homogeneous Laminated Beam Plates with Delamination

2000 ◽  
Vol 123 (1) ◽  
pp. 61-66 ◽  
Author(s):  
Le-Chung Shiau ◽  
Yuan-Shih Chen
Keyword(s):  
Mach Number ◽  
Natural Frequencies ◽  
Plate Theory ◽  
Compressive Load ◽  
Two Dimensional ◽  
Plate Model ◽  
Laminated Beam ◽  
Simply Supported ◽  
Flutter Boundary ◽  
Homogeneous Beam

The effects of in-plane load on flutter characteristics of delaminated two-dimensional homogeneous beam plates at high supersonic Mach number are investigated theoretically. Linear plate theory and quasi-steady supersonic aerodynamic theory are employed. A simple beam-plate model is developed to predict the effects of in-plane load on flutter boundaries for the delaminated beam plates with simply supported ends. Results reveal that the presence of an in-plane compressive load degrades the stiffness and natural frequencies of the plate and thereby decreases the flutter boundary for the plate. However, for certain geometry, the flutter boundaries were raised due to flutter coalescence modes of the plate altered by the presence of the in-plane load on the plate.

Four-Point Bending of Metallic I-Core Sandwich Beams With Longitudinal Girder

2019 ◽  
Author(s):  
Wenwei Hu ◽  
Jun Liu ◽  
Pan Zhang ◽  
Yuansheng Cheng
Keyword(s):  
Mechanical Properties ◽  
Finite Element ◽  
Numerical Model ◽  
Sandwich Structure ◽  
Front Face ◽  
Beam Structure ◽  
Hull Structure ◽  
Bending Load ◽  
Back Face ◽  
Bending Loads

Abstract I-core sandwich structure has great potential in the application of hull structure construction due to its high specific strength and relatively simple manufacturing process. The topic on the study of mechanical properties of I-core sandwich structure under bending loads is of interest to structural designers since the structure is often subjected to bending loads in engineering applications. In this paper, a metallic I-core sandwich beam with longitudinal girder was designed and manufactured using laser welding technique, and finally tested under four-point bend loading. The elastic-plastic behaviors and the ultimate load carrying capacity of this novel beam structure were obtained. A numerical model was developed to investigate the mechanical properties of this novel beam structure by finite element method. The results of the numerical model were compared with experimental data. Stress components of the front face and back face in the failure process were analyzed and discussed to investigate the failure of them. Results showed that the huge local bending stresses of plate caused the failure of the front face and back face. Finally, an improved scheme for the test was proposed to provide a pure bending load, which was proved by finite element simulation. All the findings aim to guide the engineering application of this structure.

Sign in / Sign up

Export Citation Format

Share Document