Bending of Beams of Arbitrary Cross Sections—Optimal Design by Analytical Formulae

2020 ◽  
pp. 67-85
Author(s):  
Federico Maria Ballo ◽  
Massimiliano Gobbi ◽  
Giampiero Mastinu ◽  
Giorgio Previati
Keyword(s):  
Optimal Design ◽  
Cross Sections ◽  
Analytical Formulae ◽  
Bending Of Beams

Analytical Formulae for Cross Sections and Rate Constants of Elementary Processes in Gases

1985 ◽  
pp. 697-704
Author(s):  
G. V. Dubrovskiy ◽  
A. V. Bogdanov ◽  
Yu. E. Gorbachev ◽  
L. F. Vyunenko ◽  
V. A. Pavlov ◽  
...  
Keyword(s):  
Cross Sections ◽  
Rate Constants ◽  
Elementary Processes ◽  
Analytical Formulae

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.

scholarly journals Equivalent photons at the LHC: pp(γγ) → ppl+l-, Pb Pb (γγ) → Pb Pb l+l-

2018 ◽  
Vol 191 ◽  
pp. 02015
Author(s):  
Mikhail Vysotsky ◽  
Evgenii Zhemchugov
Keyword(s):  
Large Hadron Collider ◽  
Cross Sections ◽  
Heavy Ions ◽  
Hadron Collider ◽  
Atlas Collaboration ◽  
Photon Collider ◽  
Analytical Formulae ◽  
Equivalent Photon

The Large Hadron Collider is considered as a photon-photon collider with the photons produced in ultraperipheral collisions of protons or heavy ions. The equivalent photon approximation is applied to derive analytical formulae for the fiducial cross sections of reactions pp(γγ) → pp μ+μ- and Pb Pb (γγ) → Pb Pb μ+μ-. The results are compared to the measurements reported by the ATLAS collaboration.

Automotive Suspensions with Additional Spring in Series with Damper: Optimal Design by Analytical Formulae

2020 ◽  
Vol 4 (3) ◽  
Author(s):  
Liunan Yang ◽  
Kesavan Ramakrishnan ◽  
Giampiero Mastinu ◽  
Giorgio Previati ◽  
Massimiliano Gobbi
Keyword(s):  
Optimal Design ◽  
In Series ◽  
Analytical Formulae

Bimodal Optimization of Compressed Columns on Elastic Foundations

1986 ◽  
Vol 53 (1) ◽  
pp. 130-134 ◽  
Author(s):  
R. H. Plaut ◽  
L. W. Johnson ◽  
N. Olhoff
Keyword(s):  
Optimal Design ◽  
Cross Sections ◽  
Variable Thickness ◽  
Buckling Load ◽  
Optimal Designs ◽  
Constant Thickness ◽  
Buckling Modes ◽  
Elastic Foundations ◽  
Bimodal Optimization ◽  
Lightweight Core

We consider columns attached to elastic foundations and compressed by axial end loads. Pinned-pinned, clamped-clamped, and pinned-clamped boundary conditions are treated. The columns have rectangular sandwich cross sections with a fixed lightweight core and identical face sheets of variable thickness. For given total volume, we optimize the variation of the thickness along the column so as to maximize the buckling load. In most cases, the optimal design is bimodal (i.e., associated with two buckling modes). The optimal designs depend on the foundation stiffness, and the largest increase in buckling load relative to a column with constant thickness is 22 percent.

A three-dimensional magnetostatics computer code for insertion devices

1998 ◽  
Vol 5 (3) ◽  
pp. 481-484 ◽  
Author(s):  
Oleg Chubar ◽  
Pascal Elleaume ◽  
Joel Chavanne
Keyword(s):  
Cross Sections ◽  
Three Dimensional ◽  
Object Oriented ◽  
Computer Code ◽  
Boundary Integral ◽  
Integral Approach ◽  
Registered Trademark ◽  
Cpu Time ◽  
Analytical Formulae ◽  
Field Integral

RADIA is a three-dimensional magnetostatics computer code optimized for the design of undulators and wigglers. It solves boundary magnetostatics problems with magnetized and current-carrying volumes using the boundary integral approach. The magnetized volumes can be arbitrary polyhedrons with non-linear (iron) or linear anisotropic (permanent magnet) characteristics. The current-carrying elements can be straight or curved blocks with rectangular cross sections. Boundary conditions are simulated by the technique of mirroring. Analytical formulae used for the computation of the field produced by a magnetized volume of a polyhedron shape are detailed. The RADIA code is written in object-oriented C++ and interfaced to Mathematica [Mathematica is a registered trademark of Wolfram Research, Inc.]. The code outperforms currently available finite-element packages with respect to the CPU time of the solver and accuracy of the field integral estimations. An application of the code to the case of a wedge-pole undulator is presented.

Bending of Beams with Nonlinear Material Characteristics

1980 ◽  
Vol 102 (4) ◽  
pp. 776-780 ◽  
Author(s):  
G. Szuladzinski
Keyword(s):  
Cross Sections ◽  
Elevated Temperatures ◽  
Strain Curve ◽  
Bending Moment ◽  
Nonlinear Material ◽  
Stress Strain ◽  
Slope Change ◽  
Deflection Analysis ◽  
Manual Methods ◽  
Bending Of Beams

When an expression is known for the curvature of a beam as a function of a bending moment, it is a simple matter to determine the deflected shape. It is a bigger problem to obtain such an explicit expression using a realistic stress-strain curve. This paper begins with a Ramberg-Osgood type of stress-strain formula, that is characterized by a continuous slope change typical of metals in elevated temperatures. A moment-curvature equation of a similar form is then developed and its accuracy is verified for several basic cross-sections. The advantage of this approach is to improve the accuracy and efficiency of deflection analysis compared with the existing manual methods.

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