Spline variant of the finite-element method for calculating shells of complex geometry

Kornishin, M. S.; Yakupov, N. M.

doi:10.1007/bf00886598

Cited by 4 publications

(2 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The considered area of the unit cube is devided into finite elements and the solution u1 = u, u2 = v и u3 = w in each of them is represented in the form of an interpolation cubic spline of three variables [4][5]:…”

Section: B)mentioning

confidence: 99%

“…Currently, many studies to assess the stress-strain state of thin-walled structures are carried out on the basis of the universal finite element method (FEM). The idea of a twodimensional spline option of the FEM, combining the idea of parametrizing the middle surface of the entire area under the question and the idea of the finite element method with bicubic approximation of the required variables within each element, was presented in [3][4][5]. To assess a stress-strain state of the elements of the thin-walled structures with local blind defects, it becomes necessary to study them in a three-dimensional formulation, in particular, as in [6][7][8][9][10][11][12][13].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

To the calculation of the toroidal shell with a local deepening on the external and on the inner surface

2021

View full text Add to dashboard Cite

Thin-walled toroidal shells are widely used in the construction During operation, various defects appear on the surface of the shells, in particular, local depressions on the outer and inner surfaces, causing stress concentration in the structure. A three-dimensional spline option of the finite element method was developed to determine the stress-strain state of a toroidal shell with a local deepening on the outer and inner surface. The numerical experiments were carried out. The regularities of the changes in a stress-strain state of the shell with the change in the geometric parameters of the deepening were noted.

show abstract

Section: B)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

To the calculation of the toroidal shell with a local deepening on the external and on the inner surface

2021

View full text Add to dashboard Cite

show abstract

A new variant of the fem for evaluation the strenght of structures of complex geometry with heterogeneous material structure

Yakupov

Kiyamov

Yakupov

et al. 2023

Case Studies in Construction Materials

View full text Add to dashboard Cite

Diagnostics of thin-walled structures of complex geometry and structure

Yakupov

2021

Struct. Mech. of Eng. Const. and Build

View full text Add to dashboard Cite

The main stages of the birth of thin-walled structures, changes in their relative thickness and mass of a unit area are given; ways of creating perfect thin-walled structures are indicated. The problems arising during the operation of thin-walled structures of complex geometry, as well as approaches and methods of their calculation are noted. To ensure trouble-free operation of a thin-walled structure with a thin-layer coating, under load and exposed to physical fields and environments, it is necessary to correctly diagnose the condition of structural elements. The spline variant of the finite element method in two-dimensional (SV FEM-2) and three-dimensional (SV FEM-3) productions is noted, as well as the synthesis of these variants - SV FEM-2 + SV FEM-3. The combination of the idea of parametrization of the entire domain and approximation of the desired variables within the element by Hermitian cubic splines makes it possible to obtain high-precision consistent finite elements. The developed variants of the finite element method make it possible to evaluate the stress-strain state of structures of complex geometry, including the calculation of multilayer, thin-walled structures with coating and local defects, as well as to take into account specific surface properties other than those of the main array. Studies of stress concentration near local depressions are considered. Two-dimensional experimental and theoretical methods are noted for evaluating the stiffness properties and adhesion of thin-walled, thin-layer and composite structural elements of complex structure, which, along with a distributed complex structure, may have distributed defects. The developments were used in solving specific tasks of a number of enterprises.

show abstract

Spline variant of the finite-element method for calculating shells of complex geometry

Cited by 4 publications

References 0 publications

To the calculation of the toroidal shell with a local deepening on the external and on the inner surface

To the calculation of the toroidal shell with a local deepening on the external and on the inner surface

A new variant of the fem for evaluation the strenght of structures of complex geometry with heterogeneous material structure

Diagnostics of thin-walled structures of complex geometry and structure

Contact Info

Product

Resources

About