The Bent Strut with Variable Cross Section

1941 ◽  
Vol 45 (362) ◽  
pp. 51-66 ◽  
Author(s):  
Jean Drymael
Keyword(s):  
Cross Section ◽  
Axial Load ◽  
Graphical Method ◽  
Variable Cross Section ◽  
Transverse Load ◽  
Variable Cross ◽  
Transverse Loads ◽  
Variable Section

SummaryA graphical method is developed for solving the problem of the beam with variable section, bent by transverse loads and an axial load. The latter may be either tensile or compressive. The beam on statically determinate supports is first dealt with, successively as regards the stress and the deformation. Then a similar procedure is followed for a beam with redundant supports. Finally, the case is studied when there is no transverse load at all, that is buckling only.

scholarly journals The lateral vibrations of bars of variable section

1917 ◽  
Vol 93 (654) ◽  
pp. 506-519 ◽  
Keyword(s):  
Cross Section ◽  
Formal Analysis ◽  
Detailed Examination ◽  
Variable Cross Section ◽  
Variable Cross ◽  
Biological Application ◽  
Lateral Vibrations ◽  
Variable Section ◽  
Set Up ◽  
The Impact

The present investigation, though strictly mathematical in character, arose in connection with a suggestion, put forward by Prof. A. Dendy and the present author in another paper communicated to the Society, that the siliceous deposits found on certain sponge spicules occurred at nodes of the spicules, regarded as vibrating rods. These vibrations, being set up and maintained by the impact of currents of water on the spicules, are necessarily of the lateral type. For the detailed examination of such a suggestion, it is necessary to obtain a comprehensive account of the positions of the funda­mental nodes on a free-free bar, as dependent on the law of variation of its cross-section. The present paper contains, in fact, the formal analysis whose results were quoted without proof in the other paper. This analysis is of considerable generality, as will appear, and the particular examples selected for purposes of illustration, together with the manner in which the variable cross-section is dealt with, have been determined by the requirements of the biological application already mentioned. One general problem is in view throughout the work, and it may be stated as follows

scholarly journals Cálculo numérico de la matriz de flexibilidades de vigas de sección variable, con elementos finitos

2020 ◽  
pp. 22-31
Author(s):  
Jaime Retama Velasco ◽  
Ricardo Heras Cruz
Keyword(s):  
Finite Elements ◽  
Numerical Method ◽  
Cross Section ◽  
Variable Cross Section ◽  
Variable Cross ◽  
Complementary Energy ◽  
First Order ◽  
Tapered Beam ◽  
Variable Section ◽  
The Cross

In this work, the flexibility properties of variable cross section beams are derived, through the application of the second theorem of Castigliano; considering the complementary energy by bending and share forces. To perform the integration of the flexibility coefficients, a numerical method, which considers the discretization of the beam domain with first order rectangular finite elements, in conjunction with the Gauss rule, is proposed. At the end of the work, the proposed method is applied to a tapered beam that has been discretized with a maximum of five finite elements. It is shown that the method is general, and that it can be applied to beams of variable section in which the cross section can be complex. The results shown that no more than 3 finite elements are needed to discretize the domain of beams in which, the ratio height-length is of the order of ten.

On the Accuracy of the Bernoulli-Euler Theory for Beams of Variable Section

1963 ◽  
Vol 30 (3) ◽  
pp. 373-378 ◽  
Author(s):  
Bruno A. Boley
Keyword(s):  
Exact Solution ◽  
Cross Section ◽  
Variable Cross Section ◽  
Variable Cross ◽  
Variable Depth ◽  
Pure Bending ◽  
Variable Section ◽  
Thin Beams ◽  
The Relationship ◽  
Derivatives Of

The stresses and deflections of thin rectangular beams of arbitrary variable depth, in pure bending, according to the theory of plane stress, are considered. They are obtained in the form of series; the first term of each series is identical with the strength-of-materials solution and the others represent the necessary correction to that theory. This form of the solution is chosen because of its convenience in the study of the relationship between the Bernoulli-Euler and the exact solution. The former is found to be quite accurate for thin beams and, when certain conditions are satisfied by the ordinates (and their spanwise derivatives) of the upper and lower edges of the beam. The Bernoulli-Euler theory is ambiguous in prescribing the position of the axis of a beam of variable cross section; admissible choices for the axis are presented.

scholarly journals SERIES SOLUTION OF LARGE DEFORMATION OF A BEAM WITH ARBITRARY VARIABLE CROSS SECTION UNDER AN AXIAL LOAD

2009 ◽  
Vol 51 (1) ◽  
pp. 10-33 ◽  
Author(s):  
SHIJUN LIAO
Keyword(s):  
Differential Equations ◽  
Cross Section ◽  
Axial Load ◽  
Nonlinear Differential Equations ◽  
Variable Cross Section ◽  
Variable Coefficients ◽  
Buckling Load ◽  
Moment Of Inertia ◽  
Variable Cross ◽  
Critical Buckling Load

AbstractA general analytic approach is proposed for nonlinear eigenvalue problems governed by nonlinear differential equations with variable coefficients. This approach is based on the homotopy analysis method for strongly nonlinear problems. As an example, a beam with arbitrary variable cross section acted on by a compressive axial load is used to show its validity and effectiveness. This approach provides us with great freedom to transfer the original nonlinear buckling equation with variable coefficients into an infinite number of linear differential equations with constant coefficients that are much easier to solve. More importantly, it provides us with a convenient way to guarantee the convergence of solution series. As an example, the beam displacement and the critical buckling load can be obtained for arbitrary variable cross sections. The influence of nonuniformity of moment of inertia is investigated in detail and the optimal distributions of moment of inertia are studied. It is found that the critical buckling load of a beam with the optimal distribution of moment of inertia can be approximately 21–22% larger than that of a uniform beam with the same average moment of inertia. Mathematically, this approach is rather general and thus can be used to solve many other linear/nonlinear differential equations with variable coefficients.

scholarly journals Work of a railway sleeper as a structure with variable cross-section - the issue of an equivalent cross-section

2018 ◽  
Vol 2018 (6) ◽  
pp. 1-12
Author(s):  
Włodzimierz Czyczuła ◽  
Dorota Błaszkiewicz ◽  
Małgorzata Urbanek
Keyword(s):  
Numerical Model ◽  
Cross Section ◽  
Real Variable ◽  
Variable Cross Section ◽  
Moment Of Inertia ◽  
Variable Cross ◽  
Bending Stress ◽  
Variable Section ◽  
Vertical Displacements ◽  
Railway Sleeper

Abstract: The article presents an analysis of the work of a sleeper as a construction with variable section, and of the method of determining an equivalent section, constant throughout the length, the utilisation of which would have similar shapes of deflection and bending stress lines in relation to the real, variable cross section. Using an analytical and a numerical model, vertical displacements and stresses for two types of sleepers – PS-94 and PS-08 – were determined. The comparison of the methods allows for calculating an equivalent moment of inertia for analytical calculations, specifically the dynamic ones.

Optimal Design of an Angular Box for a Mixed Flow Grain Dryer

2021 ◽  
Vol 37 (4) ◽  
pp. 555-562
Author(s):  
Qing Jiang ◽  
Ye Zhang ◽  
Shiyou Yan ◽  
Liangyuan Xu
Keyword(s):  
Numerical Simulation ◽  
Flow Field ◽  
Cross Section ◽  
Pressure Field ◽  
Variable Cross Section ◽  
List Type ◽  
Variable Cross ◽  
Mixed Flow ◽  
Hot Air ◽  
Variable Section

Highlights The drying effect in the drying layer is affected by the status of the flow field. The angular box of the drying oven is optimized to improve the drying effect. The structure of the variable-section angular box significantly reduced unevenness and improved the drying effect. Abstract . Dryers are subject to problems as they are unable to fully and uniformly dry grain. Considering the mixed-flow drying process and improving the drying uniformity, this study conducted a numerical simulation of the hot air temperature field, velocity field, and pressure field with ordinary equal cross-section. The dryer was optimized by a variable-section angular box structure for simulation analysis and experimental verification. The results demonstrated the following: the optimized variable cross-section angular box can improve the uniformity of the overall flow of hot air in the drying box; that is, it diffuses uniformly in the temperature, speed, and pressure field of hot air. A comparative analysis of equal cross-section and variable cross-section angled tubes indicated that the unevenness coefficient of the tubes’ wind field of the same section was reduced from 81.31% to 66.8%, 51.19% to 32.78%, and 56.98% to 42.57%, which significantly reduced unevenness and improved the drying effect. Keywords: Angular box, Flow field distribution uniformity, Grain drying, Numerical simulation.

scholarly journals Track design and realization of braiding for three-dimensional variably shaped cross-section preforms

2021 ◽  
Vol 16 ◽  
pp. 155892502110025
Author(s):  
Shao Guowei ◽  
Sun Zhihong ◽  
Zhou Qihong ◽  
Wang Zhenxi ◽  
Wang Bing ◽  
...  
Keyword(s):  
Cross Section ◽  
High Performance ◽  
Three Dimensional ◽  
Variable Cross Section ◽  
Topology Design ◽  
Variable Cross ◽  
Braided Composites ◽  
3D Braided Composites ◽  
Variable Section ◽  
Shaped Cross Section

The preforms of three-dimensional (3D) braided composites have a monolithic structure that is braided with high-performance fibers using 3D braiding technology. Compared with traditional laminate composites, braided composites are widely favored because of their superior overall performance and mechanical properties. The capability of fabricating various yarn structures with a flexible 3D rotary braiding method, however, has not been systematically investigated, especially for a variable-section braiding structure. In accordance with the principles of braiding technology and the characteristics of a 3D braiding structure, in this study, we examined a braiding technology for the production of 3D variably shaped cross-section fabric, focusing on three key factors: the topology design of tracks, the arrangement of carriers, and the matrix algorithm of the braiding of variably shaped cross sections. We calculated new kind of structural synthesis approach to a 3D braiding track for a variable section based on the carrier arrangement characteristic method and completed the entire braiding scheme of the variable cross section. In addition, this approach represents an important step toward a simplified understanding of the carrier motion and the operator-independent operation of a 3D rotary braiding machine.

Boundary element method in numerical study of three-dimensional Stokes flows in channels of arbitrary shape

2012 ◽  
Vol 9 (1) ◽  
pp. 94-97
Author(s):  
Yu.A. Itkulova
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Cross Section ◽  
Numerical Study ◽  
Three Dimensional ◽  
Cylindrical Tube ◽  
Variable Cross Section ◽  
Variable Cross ◽  
Periodic Flows ◽  
Element Method

In the present work creeping three-dimensional flows of a viscous liquid in a cylindrical tube and a channel of variable cross-section are studied. A qualitative triangulation of the surface of a cylindrical tube, a smoothed and experimental channel of a variable cross section is constructed. The problem is solved numerically using boundary element method in several modifications for a periodic and non-periodic flows. The obtained numerical results are compared with the analytical solution for the Poiseuille flow.

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