Comparison of two systems of governing equations for the thin shell analysis

Кривошапко, С. Н.; Razin, A D

doi:10.1063/5.0099905

Cited by 1 publication

(3 citation statements)

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“…Taking these conditions into consideration, one can use the system of 20 governing equations of Goldenveiser [11] of thin shell theory for arbitrary curvilinear coordinates containing internal "pseudoforces" and "pseudo-moments" or the system of governing equations suggested by Krivoshapko [12] containing internal forces and moment recalculated per unit length of curvilinear coordinates or the governing equations of Grigorenko and Timonin [13] written in tensor form. The governing equations offered by these scientists contain the coefficients of the basic quadratic forms of surfaces, which for the considered ruled shells are presented in this paper for the first time.…”

Section: Preconditions For Choosing a Methods For Determining The Par...mentioning

confidence: 99%

“…6, c The equilibrium equations of the approximate momentless thin shell theory for an arbitrary coordinate system are obtained from the equilibrium equations of the moment theory. Eliminating the bending and twisting moments and retaining the normal and tangent internal forces, we can write (Figure 7) [12]:…”

Section: Preconditions For Choosing a Methods For Determining The Par...mentioning

confidence: 99%

“…= Y = 0 for the problem in question. The full version of the equations ( 18)-( 21) is presented in [12].…”

Section: The Momentless Theory Of Analysis Of the Conical Shell Prese...mentioning

confidence: 99%

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Geometric Investigation of Three Thin Shells with Ruled Middle Surfaces with the Same Main Frame

Gbaguidi Aisse,

Aleshina,

Mamieva

2024

Struct. Mech. of Eng. Const. and Build

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It is proved and illustrated that by taking the main frame of the surface, consisting of three plane curves placed in three coordinate planes, three different algebraic surfaces with the same rigid frame can be designed. For the first time, one three of new ruled surfaces in a family of five threes of ruled surfaces, formed on the basis of some shapes of hulls of river and see ships, which, in turn, are projected in the form of algebraic surfaces with a main frame of three superellipses or of three other plane curves, is under consideration in detail with a standpoint of differential geometry. The geometrical properties of the ruled surfaces taken as the middle surfaces of thin shells for industrial and civil engineering are presented. Analytical formulas for determination of force resultants with using the approximate momentless theory of shells of zero Gaussian curvature given by non-orthogonal conjugate curvilinear coordinates are offered for the first time. The results derived using these formulae will help to correct the results obtained by numerical methods.

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Section: Preconditions For Choosing a Methods For Determining The Par...mentioning

confidence: 99%

Section: Preconditions For Choosing a Methods For Determining The Par...mentioning

confidence: 99%

See 1 more Smart Citation

Geometric Investigation of Three Thin Shells with Ruled Middle Surfaces with the Same Main Frame

Gbaguidi Aisse,

Aleshina,

Mamieva

2024

Struct. Mech. of Eng. Const. and Build

View full text Add to dashboard Cite

show abstract

Comparison of two systems of governing equations for the thin shell analysis

Cited by 1 publication

References 12 publications

Geometric Investigation of Three Thin Shells with Ruled Middle Surfaces with the Same Main Frame

Geometric Investigation of Three Thin Shells with Ruled Middle Surfaces with the Same Main Frame

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