Large Deflections and Buckling Loads of Cantilever Columns with Constant Volume

2017 ◽  
Vol 17 (08) ◽  
pp. 1750091 ◽  
Author(s):  
Joon Kyu Lee ◽  
Byoung Koo Lee
Keyword(s):  
Differential Equations ◽  
Cross Section ◽  
Large Deflection ◽  
Nonlinear Differential Equations ◽  
Constant Volume ◽  
Large Deflections ◽  
Buckling Loads ◽  
Geometrical Nonlinear ◽  
Deflection Theory ◽  
Large Deflection Theory

This paper deals with the large deflections and buckling loads of tapered cantilever columns with a constant volume. The column member has a solid regular polygonal cross-section. The depth of this cross-section is functionally varied along the column axis. Geometrical nonlinear differential equations, which govern the buckled shape of the column, are derived using the large deflection theory, considering the effect of shear deformation. The buckling load of the column is approximately equivalent to the load under which a very small tip deflection occurs. In regard to the numerical results, both the elastica and buckling loads with varying column parameters are discussed. The configurations of the strongest column are also presented.

Large Deflection Theory for Orthotropic Rectangular Plates Subjected to Edge Compression

1952 ◽  
Vol 19 (4) ◽  
pp. 446-450
Author(s):  
Syed Yusuff
Keyword(s):  
Large Deflection ◽  
Polytechnic Institute ◽  
Large Deflections ◽  
Rectangular Plates ◽  
Compression Tests ◽  
Deflection Theory ◽  
Large Deflection Theory ◽  
Theoretical Results ◽  
Anisotropic Rectangular Plates

Abstract A theory is presented of the large deflections of orthotropic (orthogonally anisotropic) rectangular plates when the plate is initially slightly curved and its boundaries are subjected to the conditions prevailing in edgewise compression tests. Results are given of computations carried out for four different combinations of load and lamination in Fiberglas panels. These theoretical results duplicate the substantial variations in the load-strain and load-deflection diagrams obtained earlier in experiments at the Polytechnic Institute of Brooklyn.

Analysis and Design of Thin Struts With Large Elastic Displacements: Part 1—Analysis of the Properties of the Solutions of the Nonlinear Differential Equations and the Behavior of the Strut

1974 ◽  
Vol 96 (3) ◽  
pp. 917-922 ◽  
Author(s):  
T. Y. Na ◽  
G. M. Kurajian ◽  
D. L. Holbert
Keyword(s):  
Differential Equations ◽  
Nonlinear Differential Equations ◽  
Elastic Behavior ◽  
Large Deflections ◽  
Transformation Technique ◽  
Analysis And Design ◽  
Engineering Aspect ◽  
Practical Engineering

Employing a transformation technique, an analysis is made of the properties of the solution of the differential equations resulting from the analysis of the elastic behavior of an eccentrically loaded thin strut. The thin strut is made to experience large deflections and the end supports are simultaneously pinned and restrained by torsional bar springs. The paper is divided into two parts. Part 1 deals primarily with the properties of the solution of the equations; and Part 2 deals with the practical engineering aspect where, employing Part 1, realistic values and ranges of parameters are assigned. The resulting design curves and tables, useful to the design engineer, are presented.

Benchmark of Plate Forming and Weld Distortion Process

2005 ◽  
Vol 128 (3) ◽  
pp. 414-419
Author(s):  
James Gombas
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Cylindrical Shell ◽  
Large Deflection ◽  
Element Analysis ◽  
Manufacturing Simulation ◽  
Simulation Process ◽  
Weld Distortion ◽  
Deflection Theory ◽  
Large Deflection Theory

A circular flat plate with a perforated central region is to be formed by dies into a dome and then welded onto a cylindrical shell. After welding, the dome must be spherical within a narrow tolerance band. This plate forming and welding is simulated using large deflection theory elastic-plastic finite element analysis. The manufacturing assessment is performed so that the dies may be designed to compensate for plate distortions that occur during various stages of manufacturing, including the effects of weld distortion. The manufacturing simulation benchmarks against measurements taken at several manufacturing stages from existing hardware. The manufacturing simulation process can then be used for future applications of similar geometries.

Application of large-deflection theory to normally loaded rectangular plates with clamped edges

1970 ◽  
Vol 5 (2) ◽  
pp. 140-144 ◽  
Author(s):  
A Scholes
Keyword(s):  
Large Deflection ◽  
Rectangular Plates ◽  
Simply Supported ◽  
Aspect Ratios ◽  
Non Linear ◽  
Deflection Theory ◽  
Large Deflection Theory ◽  
Clamped Edges ◽  
Clamped Edge ◽  
Good Agreement

A previous paper (1)∗described an analysis for plates that made use of non-linear large-deflection theory. The results of the analysis were compared with measurements of deflections and stresses in simply supported rectangular plates. In this paper the analysis has been used to calculate the stresses and deflections for clamped-edge plates and these have been compared with measurements made on plates of various aspect ratios. Good agreement has been obtained for the maximum values of these stresses and deflections. These maximum values have been plotted in such a form as to be easily usable by the designer of pressure-loaded clamped-edge rectangular plates.

scholarly journals Effect of Material Nonlinearity on Large Deflection of Variable-Arc-Length Beams Subjected to Uniform Self-Weight

2012 ◽  
Vol 2012 ◽  
pp. 1-9 ◽  
Author(s):  
Chainarong Athisakul ◽  
Boonchai Phungpaingam ◽  
Gissanachai Juntarakong ◽  
Somchai Chucheepsakul
Keyword(s):  
Differential Equations ◽  
Large Deflection ◽  
Numerical Solutions ◽  
Nonlinear Differential Equations ◽  
Optimization Technique ◽  
Material Constant ◽  
Constitutive Law ◽  
Arc Length ◽  
Stress Strain Relation ◽  
Equilibrium Configurations

This paper presents a large deflection of variable-arc-length beams, which are made from nonlinear elastic materials, subjected to its uniform self-weight. The stress-strain relation of materials obeys the Ludwick constitutive law. The governing equations of this problem, which are the nonlinear differential equations, are derived by considering the equilibrium of a differential beam element and geometric relations of a beam segment. The model formulation presented herein can be applied to several types of nonlinear elastica problems. With presence of geometric and material nonlinearities, the system of nonlinear differential equations becomes complicated. Consequently, the numerical method plays an important role in finding solutions of the presented problem. In this study, the shooting optimization technique is employed to compute the numerical solutions. From the results, it is found that there is a critical self-weight of the beam for each value of a material constantn. Two possible equilibrium configurations (i.e., stable and unstable configurations) can be found when the uniform self-weight is less than its critical value. The relationship between the material constantnand the critical self-weight of the beam is also presented.

A Model of a Trapped Particle Under a Plate Adhering to a Rigid Surface

2013 ◽  
Vol 80 (5) ◽  
Author(s):  
Joel R. Parent ◽  
George G. Adams
Keyword(s):  
Numerical Solution ◽  
Large Deflection ◽  
Nonlinear Differential Equations ◽  
Plate Thickness ◽  
Work Of Adhesion ◽  
Contact Radius ◽  
Approximate Analytic Solution ◽  
Total Potential ◽  
Curve Fit ◽  
Deflection Theory

Micro and nanomechanics are growing fields in the semiconductor and related industries. Consequently obstacles, such as particles trapped between layers, are becoming more important and warrant further attention. In this paper a numerical solution to the von Kármán equations for moderately large deflection is used to model a plate deformed due to a trapped particle lying between it and a rigid substrate. Due to the small scales involved, the effect of adhesion is included. The recently developed moment-discontinuity method is used to relate the work of adhesion to the contact radius without the explicit need to calculate the total potential energy. Three different boundary conditions are considered—the full clamp, the partial clamp, and the compliant clamp. Curve-fit equations are found for the numerical solution to the nondimensional coupled nonlinear differential equations for moderately large deflection of an axisymmetric plate. These results are found to match the small deflection theory when the deflection is less than the plate thickness. When the maximum deflection is much greater than the plate thickness, these results represent the membrane theory for which an approximate analytic solution exists.

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