Basic (Discontinuous) and Smoothing-Up (Conjugated) Solutions in Transfer-Matrix Method for Static Geometrically Nonlinear Beam and Cable in Plane

Оrynyak, І. V.; Mazuryk, Roman; Oryniak, Andrii

doi:10.1061/(asce)em.1943-7889.0001753

Cited by 6 publications

(4 citation statements)

References 32 publications

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“…The solutions (8b) and (8c) are given in form suitable for application of transfer matrix method, which is very popular in analysis of 1D problems [26], especially in structural mechanics [27]. Application of formulas (8b) and (8c) for each elementary mass section x Δ , application of conjugation (continuity) equations at the border between any neighboring mass sections:…”

Section: Description Of Semi Analytical Methods For 1-d Gas Dynamicmentioning

confidence: 99%

Semi-analytical implicit direct time integration method for 1-D gas dynamic problem

Orynyak,

Kostyushko,

Mazuryk

2023

Mech. Adv. Technol.

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Sharp wave treatment for 1-D gas dynamic problem is still a chellenge for modern numerical methods. They often require too many space and time steps, produce spurious oscillation of solution, exhibit a strong numerical dissipation or divergence of results. This paper is further extension of authors’ idea of employment the analytical solution for space coordinate, where time step is a parameter which used in the space solution. Its peculiarity consists in development of additional procedure of linearization of dependence between the pressure and density. It is performed in premise that actual pressure for each space element is close to the basic pressure, attained at previous moment of time. The efficiency of method is tested on the very popular task of Sod, where two different ideal gases in a tube are separated by diaphragm, which is suddenly broken. The problem considered in Lagrangian coordinates formulation. The results obtained show the very good efficiency of method, which requires the essentially lesser time and space steps, leads to no spurious oscillation and give consistent and predictable results with respect to meshing. The accuracy of method is mostly controlled by time step, which should be larger than clearly stated theoretical lower limit. Other advantage of method is that it can calculate the process to any desired moment of time, and space meshing can be variable in time and space and can be easily adapted during the process of calculation.

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Section: Description Of Semi Analytical Methods For 1-d Gas Dynamicmentioning

confidence: 99%

Semi-analytical implicit direct time integration method for 1-D gas dynamic problem

Orynyak,

Kostyushko,

Mazuryk

2023

Mech. Adv. Technol.

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“…It will be presented in form suitable for application of transfer matrix method [20,21]. According to it [21], solution…”

Section: Semianalytical Methodsmentioning

confidence: 99%

“…Next step is to find the partial solution. We look for specific partial solution which is to satisfy the zeroth initial conditions [21]:…”

Section: Semianalytical Methodsmentioning

confidence: 99%

Semi-analytical implicit direct time integration scheme on example of 1-D wave propagation problem

Оrynyak

Mazuryk

Tsybulskyi³

2022

Mech. Adv. Technol.

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The most common approach in dynamic analysis of engineering structures and physical phenomenas consists in finite element discretization and mathematical formulation with subsequent application of direct time integration schemes. The space interpolation functions are usually the same as in static analysis. Here on example of 1-D wave propagation problem the original implicit scheme is proposed, which contains the time interval value explicitly in space interpolation function as results of analytical solution of differential equation for considered moment of time. The displacements (solution) at two previous moments of time are approximated as polynomial functions of position and accounted for as particular solutions of the differential equation. The scheme demonstrates the perfect predictable properties as to dispersion and dissipation. The crucial scheme parameter is the time interval – the lesser the interval the more correct results are obtained. Two other parameters of the scheme – space interval and the degree of polynomial approximation have minimal impact on the general behavior of solution and have influence on small zone near the front of the wave.

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“…The peculiarity and main idea of given work consists in that beam spring splines are calculated iteratively with accounting for the big deviation and change of local basis vector system (tangent and normal) [12]. Besides the notion of fictitious points is introduced here which are not related with the real (measured) points.…”

Section: Introductionmentioning

confidence: 99%

Application of beam theory for the construction of twice differentiable closed contours based on discrete noisy points

Оrynyak¹,

Koltsov²,

Chertov³

et al. 2022

SRIT

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The smoothing of measured noisy positions of discrete points has considerable significance in various industries and computer graphic applications. The idea of work consists of the employment of the technique of beam with spring supports. The local coordinates systems are established for beam straight line segments, where the initial angles between them are accounted for in the conjugation equations, which provide the angular continuity. The notions of imaginary points are introduced, the purpose of which is to approach the real length of the smoothed contour to the length of the straight chord. Several examples of closed denoised curve reconstruction from an unstructured and highly noisy 2D point cloud are presented.

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Basic (Discontinuous) and Smoothing-Up (Conjugated) Solutions in Transfer-Matrix Method for Static Geometrically Nonlinear Beam and Cable in Plane

Cited by 6 publications

References 32 publications

Semi-analytical implicit direct time integration method for 1-D gas dynamic problem

Semi-analytical implicit direct time integration method for 1-D gas dynamic problem

Semi-analytical implicit direct time integration scheme on example of 1-D wave propagation problem

Application of beam theory for the construction of twice differentiable closed contours based on discrete noisy points

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