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

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.

On Riemann-Stieltjes integral boundary value problems of Caputo-Riemann-Liouville type fractional integro-differential equations

Under different criteria, we prove the existence and uniqueness of solutions for a Riemann-Stieltjes integro-multipoint boundary value problem of Caputo-Riemann-Liouville type fractional integrodifferential equations. Our results rely on the modern methods of functional analysis and are well-illustrated with the help of examples. Some interesting observations are also presented.

Strength optimization of structural elements by means of optimal control

This paper investigates the optimal shaping of the web height of an I-section steel portal frame. The problem is formulated as a control theory task. From a mathematical perspective, the task involves solving the multipoint boundary value problem for the system of forty-three differential equations. The solution is compared to results obtained from the finite element software Abaqus.

Existence of Weak Solutions for Fractional Integrodifferential Equations with Multipoint Boundary Conditions

By combining the techniques of fractional calculus with measure of weak noncompactness and fixed point theorem, we establish the existence of weak solutions of multipoint boundary value problem for fractional integrodifferential equations.