scholarly journals The continuation method for calculation of continuous beams of arbitrary bending rigidity

2021 ◽  
Vol 350 ◽  
pp. 00017
Author(s):  
Andrei Verameichyk ◽  
Mikhael Mazyrka ◽  
Vitaliy Khvisevich
Keyword(s):  
Optimal Design ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Continuation Method ◽  
Numerical Implementation ◽  
Bending Rigidity ◽  
Multipoint Boundary ◽  
Continuous Beams ◽  
Multipoint Boundary Value Problem

This article presents an effective mathematical continuation method for the numerical implementation of the multipoint boundary value problem, to which the calculation of a beam of arbitrary rigidity at any of its supports is reduced. The problem can be treated as a direct one in the matter of constructing an optimal design based on beam systems. A test example of the calculation is given.

scholarly journals Positive Solutions for Resonant and Nonresonant Nonlinear Third-Order Multipoint Boundary Value Problems

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Liu Yang ◽  
Chunfang Shen ◽  
Dapeng Xie
Keyword(s):  
Boundary Value Problem ◽  
Positive Solution ◽  
Positive Solutions ◽  
Boundary Value ◽  
Type Theorem ◽  
Third Order ◽  
Multipoint Boundary ◽  
Multipoint Boundary Value Problems ◽  
First Time ◽  
Multipoint Boundary Value Problem

Positive solutions for a kind of third-order multipoint boundary value problem under the nonresonant conditions and the resonant conditions are considered. In the nonresonant case, by using the Leggett-Williams fixed point theorem, the existence of at least three positive solutions is obtained. In the resonant case, by using the Leggett-Williams norm-type theorem due to O’Regan and Zima, the existence result of at least one positive solution is established. It is remarkable to point out that it is the first time that the positive solution is considered for the third-order boundary value problem at resonance. Some examples are given to demonstrate the main results of the paper.

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