Analysis of Anisotropic Beams: An Analytic Approach

2000 ◽  
Vol 68 (4) ◽  
pp. 674-678 ◽  
Author(s):  
V. Rovenski ◽  
O. Rand
Keyword(s):  
Stress Tensor ◽  
Trigonometric Series ◽  
Cross Section ◽  
Analytic Solution ◽  
Rectangular Cross Section ◽  
Composite Beams ◽  
Elastic Response ◽  
Elastic Coupling ◽  
Exponential Functions ◽  
Coupling Mechanisms

An analytic solution for the elastic response of anisotropic composite beams of rectangular cross section is presented. The formulation is based on the expression of the stress tensor components as trigonometric series and exponential functions. The ability to predict the elastic response and the corresponding elastic coupling mechanisms is well demonstrated and discussed.

scholarly journals Flat bending shape stability of the beams with variable section width

2020 ◽  
Vol 164 ◽  
pp. 02016
Author(s):  
Anastasia Lapina ◽  
Serdar Yazyev ◽  
Anton Chepurnenko ◽  
Irina Dubovitskaya
Keyword(s):  
Trigonometric Series ◽  
Cross Section ◽  
Secular Equation ◽  
Rectangular Cross Section ◽  
Twist Angle ◽  
Shape Stability ◽  
Lateral Buckling ◽  
Concentrated Force ◽  
Angle Function ◽  
Variable Section

The paper proposes a methodology for calculating lateral buckling of beams of variable rectangular cross section based on the energy approach. The technique is considered on the example of a cantilever beam of variable width with two sections under the action of a concentrated force. The twist angle function was set in the form of a trigonometric series. As a result, the problem is reduced to a generalized secular equation.

Joule Heating in Rectangular Conductors

2020 ◽  
Vol 13 (3) ◽  
Author(s):  
C. Y. Wang
Keyword(s):  
High Temperature ◽  
Aspect Ratio ◽  
Boundary Conditions ◽  
Cross Section ◽  
Joule Heating ◽  
Asymptotic Expansions ◽  
Analytic Solution ◽  
Rectangular Cross Section ◽  
Electric Resistivity ◽  
Convection Parameter

Abstract Analytic solution for nonuniform internal Joule heating in a wire of rectangular cross section is obtained. The eigenvalues for convective or weak radiative boundary conditions are accurately estimated by asymptotic expansions. The problem is governed by the aspect ratio, the convection parameter β, and a nonuniform parameter α which relates to the slope of the electric resistivity. There exists a maximum α above which the conductor would fail due to high temperature.

FREE VIBRATION ANALYSIS OF CROSS-PLY LAYERED COMPOSITE BEAMS WITH FINITE LENGTH ON ELASTIC FOUNDATION

2008 ◽  
Vol 05 (01) ◽  
pp. 21-36 ◽  
Author(s):  
RAMAZAN-ALI JAFARI-TALOOKOLAEI ◽  
MOHAMMAD-HOSSEIN KARGARNOVIN ◽  
MOHAMMAD-TAGHI AHMADIAN
Keyword(s):  
Free Vibration ◽  
Elastic Foundation ◽  
Cross Section ◽  
Finite Length ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Rectangular Cross Section ◽  
Free Vibration Analysis ◽  
Composite Beams ◽  
Layered Composite

In this paper, free vibration analysis of cross-ply layered composite beams (LCB) with finite length and rectangular cross-section rested on an elastic foundation is investigated by finite element method. Based on the Timoshenko beam theory which includes the shear deformation and rotary inertia, the stiffness and mass matrices of a LCB are obtained using the energy method. Then, the natural frequencies are calculated by employing eigenvalue technique. The obtained results are verified against existing data in the literatures for a LCB with no foundation and uniform cross-section. Good agreements are observed between these cases. In the same way, the natural frequencies of a specific case, i.e. the stepped beam are calculated and finally, free vibrations of a symmetric and non-symmetric LCB are compared with each others.

scholarly journals Designing for People’s Safety on Flooded Streets: Uncertainties and the Influence of the Cross-Section Shape, Roughness and Slopes on Hazard Criteria

Water ◽  
2021 ◽  
Vol 13 (15) ◽  
pp. 2119
Author(s):  
Luís Mesquita David ◽  
Rita Fernandes de Carvalho
Keyword(s):  
Cross Section ◽  
Overland Flow ◽  
Rectangular Cross Section ◽  
Safety Hazard ◽  
Cross Section Shape ◽  
Section Shape ◽  
Flood Flows ◽  
The Cross ◽  
Flooding Risk

Designing for exceedance events consists in designing a continuous route for overland flow to deal with flows exceeding the sewer system’s capacity and to mitigate flooding risk. A review is carried out here on flood safety/hazard criteria, which generally establish thresholds for the water depth and flood velocity, or a relationship between them. The effects of the cross-section shape, roughness and slope of streets in meeting the criteria are evaluated based on equations, graphical results and one case study. An expedited method for the verification of safety criteria based solely on flow is presented, saving efforts in detailing models and increasing confidence in the results from simplified models. The method is valid for 0.1 m2/s 0.5 m2/s. The results showed that a street with a 1.8% slope, 75 m1/3s−1 and a rectangular cross-section complies with the threshold 0.3 m2/s for twice the flow of a street with the same width but with a conventional cross-section shape. The flow will be four times greater for a 15% street slope. The results also highlighted that the flood flows can vary significantly along the streets depending on the sewers’ roughness and the flow transfers between the major and minor systems, such that the effort detailing a street’s cross-section must be balanced with all of the other sources of uncertainty.

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