A New Class of Plane Curves with Arc Length Parametrization and Its Application to Linear Analysis of Curved Beams

The objective of this paper is to define one class of plane curves with arc-length parametrization. To accomplish this, we constructed a novel class of special polynomials and special functions. These functions form a basis of L2(R) space and some of their interesting properties are discussed. The developed curves are used for the linear static analysis of curved Bernoulli–Euler beam. Due to the parametrization with arc length, the exact analytical solution can be obtained. These closed-form solutions serve as the benchmark results for the development of numerical procedures. One such example is provided in this paper.

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Analytical Solution of Thick Piezoelectric Curved Beams with Variable Curvature Considering Shearing Deformation

International Journal of Applied Mechanics ◽

10.1142/s1758825117500065 ◽

2017 ◽

Vol 09 (01) ◽

pp. 1750006 ◽

Cited By ~ 4

Author(s):

Yong Zhou ◽

Timo Nyberg ◽

Gang Xiong ◽

Shi Li ◽

Hongbo Zhou ◽

...

Keyword(s):

Closed Form ◽

Bending Moment ◽

Arc Length ◽

Curved Beams ◽

Governing Equations ◽

Displacement Fields ◽

Closed Form Solutions ◽

Shearing Deformation ◽

Equivalent Modulus ◽

Tangent Slope

In this paper, an analytical method based on Timoshenko theory is derived for obtaining the in-plane static closed-form general solutions of deep curved laminated piezoelectric beams with variable curvatures. The equivalent modulus of elasticity is utilized to take into account the material couplings in the laminated beam. The linear piezoelectric effect is considered to develop the static governing equations. The governing differential equations are formulated as functions of the angle of tangent slope by introducing the coordinate system defined by the arc length of the centroidal axis and the angle of tangent slope. To solve the governing equations, defined are the fundamental geometric properties, such as the moments of the arc length with respect to horizontal and vertical axes. As the radius is known, the fundamental geometric quantities can be calculated to obtain the static closed-form solutions of the axial force, shear force, bending moment, rotation angle, and displacement fields at any cross-section of curved beams. The closed-form solutions of the circle beams covered with piezoelectric layers under various loading cases are presented. The results show the consistency in comparison with finite results. Solutions of the non-dimensional displacements for the laminated circular and spiral curved beams with different lay-ups are available. The non-dimensional displacements with geometry and material parameters are also investigated.

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An Exact Analytical Solution of Blast Wave Problem in Gas-Dynamics at Stellar Surface

International Journal of Computer Sciences and Engineering ◽

10.26438/ijcse/v7i5.13191322 ◽

2019 ◽

Vol 7 (5) ◽

pp. 1319-1322

Author(s):

Syed Aftab Haider ◽

Akmal Husain ◽

V. K. Singh

Keyword(s):

Analytical Solution ◽

Blast Wave ◽

Gas Dynamics ◽

Exact Analytical Solution ◽

Stellar Surface ◽

Wave Problem

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The exact analytical solution of the dual-phase-lag two-temperature bioheat transfer of a skin tissue subjected to constant heat flux

Scientific Reports ◽

10.1038/s41598-020-73086-0 ◽

2020 ◽

Vol 10 (1) ◽

Author(s):

Hamdy M. Youssef ◽

Najat A. Alghamdi

Keyword(s):

Heat Flux ◽

Analytical Solution ◽

Exact Analytical Solution ◽

Constant Heat Flux ◽

Bioheat Transfer ◽

Skin Tissue ◽

Phase Lag ◽

Dual Phase ◽

Constant Heat ◽

Two Temperature

Abstract This work is dealing with the temperature reaction and response of skin tissue due to constant surface heat flux. The exact analytical solution has been obtained for the two-temperature dual-phase-lag (TTDPL) of bioheat transfer. We assumed that the skin tissue is subjected to a constant heat flux on the bounding plane of the skin surface. The separation of variables for the governing equations as a finite domain is employed. The transition temperature responses have been obtained and discussed. The results represent that the dual-phase-lag time parameter, heat flux value, and two-temperature parameter have significant effects on the dynamical and conductive temperature increment of the skin tissue. The Two-temperature dual-phase-lag (TTDPL) bioheat transfer model is a successful model to describe the behavior of the thermal wave through the skin tissue.

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