Optimal Design of an Elastic Column of Thin-Walled Cross Section

1968 ◽  
Vol 35 (2) ◽  
pp. 285-288 ◽  
Author(s):  
N. C. Huang ◽  
C. Y. Sheu
Keyword(s):  
Optimal Design ◽  
Cross Section ◽  
Wall Thickness ◽  
Cross Sections ◽  
Unit Length ◽  
Compressive Load ◽  
Median Line ◽  
Vertical Column ◽  
Thin Walled ◽  
Allowable Compressive Stress

This paper treats the optimal design of a vertical column that is built-in at the lower end. In addition to its own weight, the column is to carry an axial compressive load at its unsupported upper end. The column is to be designed as a thin-walled tube. The median line is to be the same for all cross sections; the wall thickness, though constant along the median line of any cross section, is allowed to vary along the length of the tube. Accordingly, the weight per unit length of the tube is proportional to the bending stiffness. For given length and total weight, the variation of the wall thickness along the column is to be determined to maximize the critical value of the compressive load at the upper end. The influence of a maximum allowable compressive stress on the design is also investigated.

Numerical Investigation of Cross-Section on Aluminum A6063 Thin-Walled Structures under Low-Velocity Impact Loading

2014 ◽  
Vol 1019 ◽  
pp. 96-102
Author(s):  
Ali Taherkhani ◽  
Ali Alavi Nia
Keyword(s):  
Energy Absorption ◽  
Cross Section ◽  
Cross Sections ◽  
Peak Load ◽  
Circular Cross Section ◽  
Absorption Capacity ◽  
Energy Absorption Capacity ◽  
Thin Walled Structures ◽  
Thin Walled ◽  
Crush Strength

In this study, the energy absorption capacity and crush strength of cylindrical thin-walled structures is investigated using nonlinear Finite Elements code LS-DYNA. For the thin-walled structure, Aluminum A6063 is used and its behaviour is modeled using power-law equation. In order to better investigate the performance of tubes, the simulation was also carried out on structures with other types of cross-sections such as triangle, square, rectangle, and hexagonal, and their results, namely, energy absorption, crush strength, peak load, and the displacement at the end of tubes was compared to each other. It was seen that the circular cross-section has the highest energy absorption capacity and crush strength, while they are the lowest for the triangular cross-section. It was concluded that increasing the number of sides increases the energy absorption capacity and the crush strength. On the other hand, by comparing the results between the square and rectangular cross-sections, it can be found out that eliminating the symmetry of the cross-section decreases the energy absorption capacity and the crush strength. The crush behaviour of the structure was also studied by changing the mass and the velocity of the striker, simultaneously while its total kinetic energy is kept constant. It was seen that the energy absorption of the structure is more sensitive to the striker velocity than its mass.

scholarly journals Load bearing capacity of thin-walled rectangular and I-shaped steel sections of short both empty and concrete-filled columns

2021 ◽  
Vol 15 (58) ◽  
pp. 77-85
Author(s):  
Amor Bouaricha ◽  
Naoual Handel ◽  
Aziza Boutouta ◽  
Sarah Djouimaa
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Load Capacity ◽  
Cross Sectional ◽  
Short Columns ◽  
Cross Section Area ◽  
Section Area ◽  
Specimen Height ◽  
Steel Sections ◽  
Thin Walled

In this experimental work, strength results obtained on short columns subjected to concentric loads are presented. The specimens used in the tests have made of cold-rolled, thin-walled steel. Twenty short columns of the same cross-section area and wall thickness have been tested as follows: 8 empty and 12 filled with ordinary concrete. In the aim to determine the column section geometry with the highest resistance, three different types of cross-sections have been compared: rectangular, I-shaped unreinforced and, reinforced with 100 mm spaced transversal links. The parameters studied are the specimen height and the cross-sectional steel geometry. The registered experimental results have been compared to the ultimate loads intended by Eurocode 3 for empty columns and by Eurocode 4 for compound columns. These results showed that a concrete-filled composite column had improved strength compared to the empty case. Among the three cross-section types, it has been found that I-section reinforced is the most resistant than the other two sections. Moreover, the load capacity and mode of failure have been influenced by the height of the column. Also, it had noted that the experimental strengths of the tested columns don’t agree well with the EC3 and EC4 results.

Design variation of thin-walled composite beam cross-section properties

2016 ◽  
Vol 12 (3) ◽  
pp. 558-576 ◽  
Author(s):  
Aníbal J.J. Valido ◽  
João Barradas Cardoso
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Laminated Composite ◽  
Adjoint System ◽  
Design Sensitivity ◽  
Content Type ◽  
Design Elements ◽  
Thin Walled ◽  
The Cross ◽  
Cross Section Geometry

Purpose The purpose of this paper is to present a design sensitivity analysis continuum formulation for the cross-section properties of thin-walled laminated composite beams. These properties are expressed as integrals based on the cross-section geometry, on the warping functions for torsion, on shear bending and shear warping, and on the individual stiffness of the laminates constituting the cross-section. Design/methodology/approach In order to determine its properties, the cross-section geometry is modeled by quadratic isoparametric finite elements. For design sensitivity calculations, the cross-section is modeled throughout design elements to which the element sensitivity equations correspond. Geometrically, the design elements may coincide with the laminates that constitute the cross-section. Findings The developed formulation is based on the concept of adjoint system, which suffers a specific adjoint warping for each of the properties depending on warping. The lamina orientation and the laminate thickness are selected as design variables. Originality/value The developed formulation can be applied in a unified way to open, closed or hybrid cross-sections.

scholarly journals Slender body theory for particles with non-circular cross-sections with application to particle dynamics in shear flows

2019 ◽  
Vol 877 ◽  
pp. 1098-1133 ◽  
Author(s):  
Neeraj S. Borker ◽  
Donald L. Koch
Keyword(s):  
Cross Section ◽  
Relative Motion ◽  
Cross Sections ◽  
Stokes Flow ◽  
Unit Length ◽  
Fluid Velocity ◽  
Simple Shear Flow ◽  
Slender Body Theory ◽  
Aspect Ratios ◽  
Cross Sectional Dimension

This paper presents a theory to obtain the force per unit length acting on a slender filament with a non-circular cross-section moving in a fluid at low Reynolds number. Using a regular perturbation of the inner solution, we show that the force per unit length has $O(1/\ln (2A))+O(\unicode[STIX]{x1D6FC}/\ln ^{2}(2A))$ contributions driven by the relative motion of the particle and the local fluid velocity and an $O(\unicode[STIX]{x1D6FC}/(\ln (2A)A))$ contribution driven by the gradient in the imposed fluid velocity. Here, the aspect ratio ($A=l/a_{0}$) is defined as the ratio of the particle size ($l$) to the cross-sectional dimension ($a_{0}$) and $\unicode[STIX]{x1D6FC}$ is the amplitude of the non-circular perturbation. Using thought experiments, we show that two-lobed and three-lobed cross-sections affect the response to relative motion and velocity gradients, respectively. A two-dimensional Stokes flow calculation is used to extend the perturbation analysis to cross-sections that deviate significantly from a circle (i.e. $\unicode[STIX]{x1D6FC}\sim O(1)$). We demonstrate the ability of our method to accurately compute the resistance to translation and rotation of a slender triaxial ellipsoid. Furthermore, we illustrate novel dynamics of straight rods in a simple shear flow that translate and rotate quasi-periodically if they have two-lobed cross-section, and rotate chaotically and translate diffusively if they have a combination of two- and three-lobed cross-sections. Finally, we show the remarkable ability of our theory to accurately predict the motion of rings, retaining great accuracy for moderate aspect ratios (${\sim}10$) and cross-sections that deviate significantly from a circle, thereby making our theory a computationally inexpensive alternative to other Stokes flow solvers.

Collapse study of thin-walled polygonal section columns subjected to oblique loads

2007 ◽  
Vol 221 (7) ◽  
pp. 801-810 ◽  
Author(s):  
P Hosseini-Tehrani ◽  
S Pirmohammad
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Rigid Wall ◽  
Point Of View ◽  
Explicit Finite Element ◽  
Thin Walled ◽  
Oblique Load ◽  
Crash Behaviour ◽  
Vehicle Crashworthiness ◽  
Load Conditions

The present paper deals with the collapse simulation of aluminium alloy extruded polygonal section columns subjected to oblique loads. Oblique load conditions in numerical simulations are applied by means of impacting a declined rigid wall on the tubes with no friction in this task. The explicit finite element code LS-DYNA is used to simulate the crash behaviour of polygonal section columns that are undergoing both axial and bending collapse situations. In order to validate LS-DYNA results the collapse procedure of square columns is successfully simulated and the obtained numerical results are compared with actual available experimental data. Mean crush loads and permanent displacements corresponding to load angles have been investigated, considering columns with square, hexagonal, octagonal, decagonal, and circular cross-sections. It is shown that the octagonal cross-section has better characteristics from the point of view of vehicle crashworthiness under oblique load conditions.

scholarly journals Optimal Design of Single-Layered Reinforced Cylindrical Shells

2021 ◽  
Vol 24 (1) ◽  
pp. 58-64
Author(s):  
Heorhii V. Filatov ◽  
Keyword(s):  
Optimal Design ◽  
Numerical Experiment ◽  
Wall Thickness ◽  
Random Search ◽  
Cylindrical Shells ◽  
Compressive Load ◽  
Mathematical Programming Problem ◽  
Feasible Region ◽  
Shell Weight ◽  
Longitudinal Stiffeners

This paper discusses the application of the random search method for the optimal design of single-layered reinforced cylindrical shells operating in a neutral environment. When setting a mathematical programming problem, the minimum shell weight is considered as an objective function. The critical stresses are determined according to the linear theory in the elastic region of the material. As the constraints imposed on the feasible region, the constraints on the strength, general buckling and partial buckling of a shell are accepted. The aim of this paper is to study the weight efficiency of various types of shell reinforcements and the influence of an optimum-weight shell on the parameters of an axially-compressed one. A numerical experiment was carried out. Dependencies of shell weight, wall thickness, and reinforcement parameters on the magnitude of a compressive load were investigated for shells with different types of reinforcement. As a result of the numerical experiment performed, it was found that with an increase in compressive load magnitude, there is a tendency to an increase in the wall thickness of an optimal shell, with an increase in the thickness of longitudinal stiffeners (stringers) and a slight decrease in the number of ribs. In addition, it should be noted that the general case of buckling and the first special one turned out to be decisive in choosing optimal shell parameters.

The Bending of Pretwisted Thin-Walled Beams of Symmetric Star-Shaped Cross Sections

1958 ◽  
Vol 25 (1) ◽  
pp. 67-74
Author(s):  
L. Maunder
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Energy Methods ◽  
Approximate Analysis ◽  
Moments Of Inertia ◽  
Elastic Bending ◽  
Principal Moments Of Inertia ◽  
Equivalent Bending Stiffness ◽  
Symmetric Star ◽  
Thin Walled

Abstract The customary method of determining the elastic bending deflections of pretwisted beams predicts that the deflections of a uniform beam with a cross section having equal principal moments of inertia will be independent of pretwist. Experimental deflections of a thin-walled pretwisted beam with a doubly symmetric cruciform cross section have been found, however, to be significantly larger than those thus predicted. Based on energy methods, an approximate analysis is developed for pretwisted thin-walled beams having symmetric star-shaped cross sections, which takes into account the effect of interactions between pretwist and distortions of cross sections. An equivalent bending stiffness is derived which is a function of pretwist. The principal theoretical and experimental results are shown in Fig. 4.

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