Elastic critical force of centrically loaded member with asymmetric and monosymmetric cross-sections at various boundary conditions: A parametric study

2019 ◽  
Vol 184 ◽  
pp. 329-344 ◽  
Author(s):  
Michal Kováč ◽  
Ivan Baláž
Keyword(s):  
Boundary Conditions ◽  
Cross Sections ◽  
Parametric Study ◽  
Critical Force ◽  
Various Boundary Conditions

Torsional-Flexural Critical Force for Various Boundary Conditions

2016 ◽  
Vol 710 ◽  
pp. 303-308 ◽  
Author(s):  
Ivan Balaz ◽  
Michal Kovac ◽  
Tomáš Živner ◽  
Yvona Kolekova
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Approximate Method ◽  
Cross Sections ◽  
Critical Force ◽  
Various Boundary Conditions ◽  
Element Method

The system of governing differential equations of stability of members with the rigid open cross-sections was developed by Vlasov [1] in 1940. Goľdenvejzer [2] published in 1941 solution of this system by an approximate method. He proposed formula for torsional-flexural critical force Ncr.TF calculation which is modified and used in EN 1999-1-1 [3] (I.19). By introducing factor αzw he take into account any combination of boundary conditions (BCs).The purpose of this paper is to verify this formula and explore the possibility to improve the factor αzw. In the large parametrical study the authors investigated a lot of different shape of cross-sections, all 100 theoretical possible combinations of BCs and various member lengths. All results are evaluated regarding the reference results by finite element method (FEM).

Elastic Critical Force for Torsional-Flexural Buckling of Metal Members with Mono-Symmetric Cross-Sections

2015 ◽  
Vol 769 ◽  
pp. 36-42
Author(s):  
Michal Kovac
Keyword(s):  
Boundary Conditions ◽  
Approximate Method ◽  
Cross Section ◽  
Cross Sections ◽  
Parametric Study ◽  
Critical Force ◽  
Flexural Buckling ◽  
Fem Method ◽  
Thin Walled ◽  
Open Cross Section

The paper deals with torsional-flexural buckling of thin-walled metal members with mono-symmetric open cross-sections and with various torsional and flexural boundary conditions. An approximate method, which is located in recent norms, for calculation of critical forces of such member cases are focused on. For chosen type of mono-symmetric open cross-section a parametric study of critical forces by the approximate method and by as a reference taken FEM method are performed.

Nonlinear Vibrations of Beams, Strings, Plates, and Membranes Without Initial Tension

2004 ◽  
Vol 71 (4) ◽  
pp. 551-559 ◽  
Author(s):  
Zhongping Bao ◽  
Subrata Mukherjee ◽  
Max Roman ◽  
Nadine Aubry
Keyword(s):  
Boundary Conditions ◽  
Young’S Modulus ◽  
Cross Sections ◽  
Nonlinear Vibrations ◽  
Young's Modulus ◽  
Thin Plates ◽  
Radius Of Gyration ◽  
Initial Tension ◽  
Various Boundary Conditions ◽  
Analytical Expressions

The subject of this paper is nonlinear vibrations of beams, strings (defined as beams with very thin uniform cross sections), plates and membranes (defined as very thin plates) without initial tension. Such problems are of great current interest in minute structures with some dimensions in the range of nanometers (nm) to micrometers (μm). A general discussion of these problems is followed by finite element method (FEM) analyses of beams and square plates with different boundary conditions. It is shown that the common practice of neglecting the bending stiffness of strings and membranes, while permissible in the presence of significant initial tension, is not appropriate in the case of nonlinear vibrations of such objects, with no initial tension, and with moderately large amplitude (of the order of the diameter of a string or the thickness of a plate). Approximate, but accurate analytical expressions are presented in this paper for the ratio of the nonlinear to the linear natural fundamental frequency of beams and plates, as functions of the ratio of amplitude to radius of gyration for beams, or the ratio of amplitude to thickness for square plates, for various boundary conditions. These expressions are independent of system parameters—the Young’s modulus, density, length, and radius of gyration for beams; the Young’s modulus, density, length of side, and thickness for square plates. (The plate formula exhibits explicit dependence on the Poisson’s ratio.) It is expected that these results will prove to be useful for the design of macro as well as micro and nano structures.

Strongest Columns and Isoperimetric Inequalities for Eigenvalues

1962 ◽  
Vol 29 (1) ◽  
pp. 159-164 ◽  
Author(s):  
I. Tadjbakhsh ◽  
J. B. Keller
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Ordinary Differential Equations ◽  
Cross Sections ◽  
Isoperimetric Inequalities ◽  
Second Order ◽  
Buckling Load ◽  
The Other ◽  
Critical Buckling Load ◽  
Various Boundary Conditions

We consider the problem of determining what shape column has the largest critical buckling load of all columns of given length and volume. This problem was previously solved for a column hinged (pinned) at both ends. We solve it for columns clamped at one end and clamped, hinged, or free at the other end, assuming that all cross sections of the column are similar and similarly oriented. We also prove that the column previously obtained in the hinged-hinged case is actually strongest and not merely stationary. Graphs of the areas of the strongest columns as functions of distance along the columns are given for the various cases. The results are also expressed as isoperimetric inequalities for eigenvalues of second-order ordinary differential equations with various boundary conditions. Certain additional inequalities of this type are also obtained.

Ultimate Strength and Post-Ultimate Strength Behavior of Damaged Tubular Members in Offshore Structures

1988 ◽  
Vol 110 (3) ◽  
pp. 254-262 ◽  
Author(s):  
T. Yao ◽  
J. Taby ◽  
T. Moan
Keyword(s):  
Boundary Conditions ◽  
Ultimate Strength ◽  
Parametric Study ◽  
Structural Unit ◽  
Offshore Structures ◽  
Experimental Results ◽  
Lateral Deflection ◽  
Various Boundary Conditions ◽  
Unit Model ◽  
Strength Behavior

An idealized structural unit model is constructed to represent the pre and post-ultimate strength behavior of a damaged tubular member with various boundary conditions subjected to various end loads. Local denting and overall permanent lateral deflection are considered as a damage. The calculated results using this model are compared with a large number of previous and new experimental results. A parametric study regarding the influence of damages on the ultimate strength of tubular members is also performed.

Upon Impact Numerical Modeling of Foam Materials

2017 ◽  
Vol 54 (2) ◽  
pp. 195-202
Author(s):  
Vasile Nastasescu ◽  
Silvia Marzavan
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Modeling ◽  
Numerical Analysis ◽  
Numerical Methods ◽  
Boundary Conditions ◽  
General Character ◽  
Foam Material ◽  
Various Boundary Conditions ◽  
Specific Behaviour

The paper presents some theoretical and practical issues, particularly useful to users of numerical methods, especially finite element method for the behaviour modelling of the foam materials. Given the characteristics of specific behaviour of the foam materials, the requirement which has to be taken into consideration is the compression, inclusive impact with bodies more rigid then a foam material, when this is used alone or in combination with other materials in the form of composite laminated with various boundary conditions. The results and conclusions presented in this paper are the results of our investigations in the field and relates to the use of LS-Dyna program, but many observations, findings and conclusions, have a general character, valid for use of any numerical analysis by FEM programs.

Analytic solutions of the scattering by two multilayered dielectric spheres

1992 ◽  
Vol 70 (9) ◽  
pp. 696-705 ◽  
Author(s):  
A-K. Hamid ◽  
I. R. Ciric ◽  
M. Hamid
Keyword(s):  
Boundary Conditions ◽  
Cross Sections ◽  
Plane Electromagnetic Wave ◽  
Expansion Method ◽  
Analytic Solutions ◽  
Addition Theorem ◽  
Modal Expansion ◽  
Modal Expansion Method ◽  
Dielectric Spheres ◽  
Scattered Fields

The problem of plane electromagnetic wave scattering by two concentrically layered dielectric spheres is investigated analytically using the modal expansion method. Two different solutions to this problem are obtained. In the first solution the boundary conditions are satisfied simultaneously at all spherical interfaces, while in the second solution an iterative approach is used and the boundary conditions are satisfied successively for each iteration. To impose the boundary conditions at the outer surface of the spheres, the translation addition theorem of the spherical vector wave functions is employed to express the scattered fields by one sphere in the coordiante system of the other sphere. Numerical results for the bistatic and back-scattering cross sections are presented graphically for various sphere sizes, layer thicknesses and permittivities, and angles of incidence.

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