Strength and stability of geometrically nonlinear orthotropic shell structures

Semenov, Alexey

doi:10.1016/j.tws.2016.05.018

Cited by 15 publications

(7 citation statements)

References 26 publications

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“…In this paper, for the study of shell structures, it is proposed to use an algorithm based on the Ritz method and the method of continuing the solution with respect to the best parameter (Semenov (2016)).…”

Section: Methodsmentioning

confidence: 99%

Buckling of Shallow Shells of Double Curvature Stiffened by Ribs From the Outside

Семенов¹

2022

JSSCM

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The results of a computational experiment on the analysis of the effectiveness of placing stiffeners on the outer side of the shell structure are presented. The calculations were carried out on the basis of a geometrically nonlinear mathematical model that takes into account transverse shears and orthotropy of the material. The calculation algorithm is based on the Ritz method and the method of continuing the solution with respect to the best parameter. To take into account stiffeners, the refined discrete method, proposed by the author earlier, is used. Shallow shells of double curvature are analyzed. The structures are made of steel and are simply supported, the stiffening ribs are arranged orthogonally. The values of critical buckling loads are presented. The effectiveness of the location of the stiffeners on the outer side of the shell structure is shown. It is revealed that the location of the ribs on the outside increases the value of the critical buckling load.

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Section: Methodsmentioning

confidence: 99%

Buckling of Shallow Shells of Double Curvature Stiffened by Ribs From the Outside

Семенов¹

2022

JSSCM

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“…Let us use a mathematical model of the Timoshenko (Mindlin-Reissner) type, which takes into account transverse shears, material orthotropy, and geometric nonlinearity [12]. According to this model, in the case of static problems, three functions characterizing displacement of the coordinate surface points ( ) ( ) ( ) U x, y ,V x, y ,W x, y and two functions characterizing the normal rotation angles in the planes xOz , yOz , ( ( ) ( )…”

Section: Mathematical Modelmentioning

confidence: 99%

“…The authors of the monograph suggest substituting the last row ( ) T dX/dλ in the matrix of the system (15) with vector ( ) T * dX /dλ , which at each step is considered equal to the vector calculated in the previous step. We can then proceed with the explicit scheme of the Euler method to solve the initial problem (15), (12) in the form of a system of linear algebraic equations with respect to ( ) T dX/dλ [22].…”

Section: Static Problemsmentioning

confidence: 99%

Mathematical Modeling in Shell Structure Analysis Tasks

2022

IJEM

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Studying shell structures while accounting for all necessary factors is a significantly nonlinear problem that requires serious mathematical tools and sufficient computing capacities. We propose an approach to solving such problems based on the following numerical methods. We propose the use of the Ritz method, the best parameter continuation method, and the Euler method under static loading. Under dynamic loading, the Kantorovich and the Rosenbrock methods are used. Software implementation was carried out using the Maple analytical software package. This paper also provides examples of simulating the deformation process in shell structures.

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“…(complete expression is given in [2,17]) is approximated by the function of several variables, and it is sufficient to use the approximation functions and the numeric coefficients' values ensuring the minimum of the functional to recover the SSS analysis data.…”

Section: Sss Of a Shellmentioning

confidence: 99%

Stress-strain state interactive visualization of the parametrically-defined thin-shell structures with the use of AR and VR technologies

Semenov¹,

Zgoda²

2020

Self Cite

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The paper describes a mathematical model of changes in the geometry of thin-shell structures for visualization of the analysis data on their stress-strain state (SSS). Based on this mathematical model, a module for shell SSS visualization using VR and AR technologies was developed. The interactive visualization environment Unity 2019.3 and C# programming language were used. The interactive visualization module makes a 3D image of a shell structure and visualizes the SSS either through heat maps over the shell or through the changes in the shell geometry via the shell type, its geometric characteristics, and SSS analysis data (transferred to the visualization module by means of a JSON file). While working on the visualization module, the authors developed a software system that makes it possible to visualize any 3D surface with coordinate axes (including numbers with a pitch determined automatically), visualize heat maps with a graduated scale, visualize a mesh over the graph to improve the perception of the surface deformations. The middle surface deformation can also performed via SSS analysis data. This solution increases the efficiency of the work of specialists in civil engineering and architecture and can be used when training specialists in courses on thin-shell structures and procedural geometry.

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Strength and stability of geometrically nonlinear orthotropic shell structures

Cited by 15 publications

References 26 publications

Buckling of Shallow Shells of Double Curvature Stiffened by Ribs From the Outside

Buckling of Shallow Shells of Double Curvature Stiffened by Ribs From the Outside

Mathematical Modeling in Shell Structure Analysis Tasks

Stress-strain state interactive visualization of the parametrically-defined thin-shell structures with the use of AR and VR technologies

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