Finite element analysis of shells of revolution using triangular discretization elements with corrective Lagrange multipliers

Klochkov, Yu. V.; Николаев, А. П.; Vakhnina, O. V.

doi:10.3103/s0027133016050034

Cited by 6 publications

(4 citation statements)

References 4 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…where [А] is a matrix containing polynomial functions of the form. Applying to (25) the procedure of minimization with respect to {𝑊 𝑦 } 𝑇 , we can obtain the following matrix relation…”

Section: Resultsmentioning

confidence: 99%

See 1 more Smart Citation

The use of thin-walled structures for the sustainable development of agro-industrial systems and facilities

Klochkov

Николаев

Ishchanov

et al. 2022

IOP Conf. Ser.: Earth Environ. Sci.

View full text Add to dashboard Cite

The issues of optimal use of strength resources of materials from which elements of thin-walled objects of the agro-industrial complex are made for the purpose of sustainable development of agricultural production are currently coming to the fore. In this regard, the development of modern algorithms for the numerical analysis of the processes of physically nonlinear deformation of thin-walled objects of agro-industrial complex of various sizes and shapes is becoming a rather urgent topic. The article proposes an algorithm for the finite element analysis of physically nonlinear deformation of thin-walled objects of the agro-industrial complex, taking into account the transverse shear, based on the hypotheses of the theory of plastic flow The element of discretization of the thin-walled object of the agricultural and industrial complex was a four-node fragment of its middle surface. The stiffness matrix of this sampling unit was obtained in the process of minimizing the Lagrange functional with respect to the sought nodal parameters, which were the components of the step vector of displacement and their first-order partial derivatives, as well as the components of the step vector of the angles of rotation of the normal.

show abstract

Section: Resultsmentioning

confidence: 99%

“…Using the fundamental formula of continuum mechanics [25], one can obtain expressions for the covariant components of the strain increment tensor at the point М 0ζ of a thin-walled AIC object after the (n + 1)-th loading step…”

Section: Geometric Relationshipsmentioning

confidence: 99%

The use of thin-walled structures for the sustainable development of agro-industrial systems and facilities

Klochkov

Николаев

Ishchanov

et al. 2022

IOP Conf. Ser.: Earth Environ. Sci.

View full text Add to dashboard Cite

show abstract

“…When taking into account the plastic stage of deformation of the applied structural material, the deformation theory of plasticity or the theory of plastic flow is usually used. In this work, the deformation theory of plasticity was used, according to the hypotheses of which [20], we can write the following relation ( ) (8) where ( )…”

Section: Physical Relationshipsmentioning

confidence: 99%

“…To reduce the payback period of such systems, the optimal design of objects and systems for reclamation purposes becomes very important, which is unthinkable without the use of modern numerical methods of calculation [1,2,3,4,5], which, in particular, includes the finite element method (FEM) [6,7,8,9]. Moreover, the application of this method at the present stage is based on the use as discretization elements, mainly, three-dimensional finite elements [10,11,12,13,14], as the most versatile, adapted for modeling both thin-walled fragments of reclamation structures (pipelines, tanks, tanks) and thick-walled massive bodies (dams, retaining walls, joints and others).…”

Section: Introductionmentioning

confidence: 99%

Finite element modeling of the processes of elastic-plastic deformation of reclamation objects of the agro-industrial complex

Klochkov

Fomin

Vakhnina

et al. 2022

IOP Conf. Ser.: Earth Environ. Sci.

View full text Add to dashboard Cite

Annotation. To study the processes of nonlinear deformation of reclamation objects and engineering systems of the agro-industrial complex, taking into account the plastic stage of the used structural material, a finite element model was created based on a volumetric prismatic discretization element with quadrangular bases. The plastic stage of deformation of the applied structural material of the object is taken into account on the basis of the provisions of the deformation theory of plasticity. The plasticity matrix at the (j + 1)-th stage of sequential loading was compiled as a result of applying the operation of differentiating the stress tensor components accumulated over the j previous stages of sequential loading with respect to the strain tensor components. The stiffness matrix and the column of nodal forces of a prismatic discretization element with quadrangular bases at the (j + 1)-th stage of loading were obtained by minimizing the Lagrange functional. Numerical experiments on the calculation of a tubular outlet proved the adequacy of the developed finite element model and the accuracy of calculating the required strength parameters of the studied reclamation objects and other engineering systems of the agro-industrial complex, sufficient for engineering practice.

show abstract

Algorithm of finite elemental SSS analysis of thin-walled technosphere objects based on a triangular discretion element with elastic-plastic deformation

Klochkov

Vakhnina

Sobolevskaya

et al. 2021

J. Phys.: Conf. Ser.

View full text Add to dashboard Cite

Finite element analysis of shells of revolution using triangular discretization elements with corrective Lagrange multipliers

Cited by 6 publications

References 4 publications

The use of thin-walled structures for the sustainable development of agro-industrial systems and facilities

The use of thin-walled structures for the sustainable development of agro-industrial systems and facilities

Finite element modeling of the processes of elastic-plastic deformation of reclamation objects of the agro-industrial complex

Algorithm of finite elemental SSS analysis of thin-walled technosphere objects based on a triangular discretion element with elastic-plastic deformation

Contact Info

Product

Resources

About