Construction of a general solution for a system of equilibrium equations of plates made of reinforced materials

1982 ◽  
Vol 18 (5) ◽  
pp. 450-456
Author(s):  
I. Yu. Khoma ◽  
Z. A. Medvedeva
Keyword(s):  
General Solution ◽  
Equilibrium Equations ◽  
System Of Equilibrium Equations ◽  
Reinforced Materials

Boundary Integral Equation Methods for a Refined Model of Elastic Plates

2006 ◽  
Vol 11 (6) ◽  
pp. 642-654
Author(s):  
Radu Mitric ◽  
Christian Constanda
Keyword(s):  
Integral Equation ◽  
Boundary Integral Equation ◽  
Boundary Integral ◽  
Normal Strain ◽  
Elastic Plates ◽  
Equilibrium Equations ◽  
Neumann Problems ◽  
Integral Equation Methods ◽  
Transverse Normal Strain ◽  
System Of Equilibrium Equations

A theory of bending of elastic plates is considered, in which the effect of transverse shear deformation and transverse normal strain are taken into account through a specific form of the displacement field. It is shown that the system of equilibrium equations is elliptic and that Betti and Somigliana formulae can be established, which permit the solution of the interior and exterior Dirichlet and Neumann problems by means of boundary integral equation methods.

scholarly journals The Replication Hypothesis along the Take-Off Run and a System of Equilibrium Equations at the Lift-Off of a Protobird

Aerospace ◽  
2019 ◽  
Vol 6 (2) ◽  
pp. 21
Author(s):  
Phillip Burgers
Keyword(s):  
Experimental Data ◽  
Time Span ◽  
Flapping Wings ◽  
Equilibrium Equations ◽  
Scaling Down ◽  
Lift Off ◽  
To Come ◽  
System Of Equilibrium Equations

An extant bird resorts to flapping and running along its take-off run to generate lift and thrust in order to reach the minimum required wing velocity speed required for lift-off. This paper introduces the replication hypothesis that posits that the variation of lift relative to the thrust generated by the flapping wings of an extant bird, along its take-off run, replicates the variation of lift relative to the thrust by the flapping wings of a protobird as it evolves towards sustained flight. The replication hypothesis combines experimental data from extant birds with evidence from the paleontological record of protobirds to come up with a physics-based model of its evolution towards sustained flight while scaling down the time span from millions of years to a few seconds. A second hypothesis states that the vertical and horizontal forces acting on a protobird when it first encounters lift-off are in equilibrium as the protobird exerts its maximum available power for flapping, equaling its lift with its weight, and its thrust with its drag.

scholarly journals Form-Finding of Tensegrity Model with Triangular Cells

2018 ◽  
Vol 7 (3.36) ◽  
pp. 137
Author(s):  
Nur Farizah Filzah Naing ◽  
Oh Chai Lian ◽  
Ilyani Akmar Abu Bakar ◽  
Mohd Raizamzamani Md Zain
Keyword(s):  
Inverse Method ◽  
Equilibrium Equations ◽  
Form Finding ◽  
Tensegrity Structures ◽  
Weight Structure ◽  
Tensegrity Model ◽  
Generalized Inverse Method ◽  
Stage Class ◽  
System Of Equilibrium Equations ◽  
Finding Method

Tensegrity structures is a light-weight structure compared to concrete structures that are heavy and rigid in shape. The studies on form-finding for tensegrity configuration are still ongoing and have been extensively conducted. Additionally, many proposed tensegrity structures have not been built for real applications. This study aims to determine potential self-equilibrated configurations of three-stage Class I tensegrity model assemblage with triangular cells, which may be applied as deployable towers. The form-finding methodology involves phases in establishment of desired form and formulation for the self-equilibrated state. The system of equilibrium equations was solved by Moore-Penrose generalized inverse method.  A range of twist angles 10o – 50o for triangular cells was investigated in the form-finding process.  It was found that the form-finding method via changing of twist angles has successfully search self-equilibrated tensegrity models.  

A note on the infinitely deep dam with a Markovian input

1979 ◽  
Vol 16 (4) ◽  
pp. 917-922 ◽  
Author(s):  
R. M. Phatarfod
Keyword(s):  
Markov Chain ◽  
General Solution ◽  
Unit Disc ◽  
Linear Constraints ◽  
Equilibrium Equations ◽  
Ergodic Markov Chain

In this paper we consider an infinitely deep dam fed by inputs which form an ergodic Markov chain and whose release M is non-unit. The extension to non-unit release follows on lines similar to the independent inputs case. We show that P(θ) – θ MΙ where P(θ) = (pijθ i) has a maximum of N = M(M + l)/2 non-zero singularities in the unit disc, so that the general solution of the equilibrium equations has N unknown constants. We also show that these constants satisfy N linear constraints, so that the solution is fully determined.

The Morley-Koiter Equations for Thin-Walled Circular Cylindrical Shells: Part 1—General Solution for Symmetrical Shells of Uniform Thickness

1973 ◽  
Vol 40 (4) ◽  
pp. 961-965 ◽  
Author(s):  
C. P. Mangelsdorf
Keyword(s):  
General Solution ◽  
Evaluation Procedure ◽  
Uniform Thickness ◽  
Equilibrium Equations ◽  
Line Load ◽  
Longitudinal Line ◽  
Symmetrical Loading ◽  
Circular Cylindrical Shells ◽  
Simple Supports ◽  
Thin Walled

Modified Donnell equilibrium equations are solved in Part 1 for the case of symmetrical loading and supports, using Fourier series. An evaluation procedure for simple, fixed, and relaxed simple conditions is suggested. In Part 2, an application of the general solution is made for a shell with small circumferential grooves (or ribs) subjected to a longitudinal line load after approximations to allow for such grooves are introduced. The solution is completed for the boundary conditions of classical simple supports and relaxed simple supports and the results compared with experimental data.

scholarly journals A New Form of the General Solution of the Elastic Space Axisymmetric Problem in Pavement Mechanics

2016 ◽  
Vol 2016 ◽  
pp. 1-6
Author(s):  
Jia Liang ◽  
Guo Jian ◽  
He Shikai
Keyword(s):  
General Solution ◽  
Axisymmetric Problem ◽  
Hankel Transform ◽  
Elastic Half Space ◽  
Displacement Function ◽  
Winkler Foundation ◽  
Elastic Space ◽  
Equilibrium Equations ◽  
Present Solution ◽  
New Form

In order to analyze the stress and displacement of pavement, a new form of the general solution of the elastic space axisymmetric problem is proposed by the method of mathematics reasoning. Depending on the displacement function put forward by Southwell, displacement function is derived based on Hankel transform and inverse Hankel transform. A new form of the general solution of the elastic space axisymmetric problem has been set up according to a few basic equations as the geometric equations, constitutive equations, and equilibrium equations. The present solution applies to elastic half-space foundation and Winkler foundation; the stress and displacement of pavement are obtained by mathematical deduction. The example results show that the proposed method is practically feasible.

On Some Classes of Correct Problems in the Membrane Theory of Convex Shells

2020 ◽  
pp. 25-29
Author(s):  
E.V. Tyurikov
Keyword(s):  
Smooth Boundary ◽  
Hilbert Problem ◽  
Boundary Value ◽  
Geometric Description ◽  
Membrane Theory ◽  
Equilibrium Equations ◽  
Wide Family ◽  
Boundary Solutions ◽  
System Of Equilibrium Equations ◽  
Riemann Hilbert Problem

On the basis of the theory of the modified Riemann-Hilbert problem for generalized analytic functions, a geometric description is given of a fairly wide family of correct by I. N. Vekua of boundary value problems of the membrane theory of convex hulls with a piecewise smooth boundary. Solutions to the corresponding Riemann-Hilbert problem for an elliptic system of equilibrium equations are found in the classes of N.I. Muskhelishvili and realize a state of tense equilibrium under the condition of stress concentration in corner points. An effective formula is given for calculating the index of the boundary condition, which allows us to formulate the results in a visible form. Families of shells are found for which the solvability picture of the main boundary-value problem coincides with the solvability picture of the Vekua problem for shells with a smooth border.

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