Solutions of Static Problems Based on the Refined Model

Grigorenko, А. Ya.; Müller, Wolfgang; Grigorenko, Yaroslav M.; Vlaikov, Georgii G.

doi:10.1007/978-981-10-0645-6_1

Cited by 3 publications

(8 citation statements)

References 16 publications

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“…In ratios for deformations (4) the relationship between deformations and displacements is presented. Reversed to ratios elasticity (3) dependencies deformations from tensions let's introduce as…”

Section: Statement Of the Problem And Methods Of Solutionmentioning

confidence: 99%

Stability of cylindrical anisotropic composite shells under torsion in a three-dimensional formulation

Trach,

Podvornyi

2023

OMTC

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The article presents a calculation of the stability of non-thin cylindrical anisotropic layered shells under the action of end torsional moments in a spatial formulation. The anisotropy of the used material is characterized by one plane of elastic symmetry of characteristics. This is caused by the mismatch between the main elastic directions of the composite fibrous orthotropic material and the axes of the curvilinear cylindrical coordinate system. A three-dimensional inhomogeneous system of partial differential equations describing the subcritical stress-strain state within the linear theory of elasticity is derived using the Hu-Washizu variational principle. Reducing the dimension of the problem under consideration from three-dimensional to one-dimensional is carried out by taking into account the axial symmetry of the deformation of the cylindrical shell and using the method of straight lines along the generatrix. Based on the modified Hu-Washizu variational principle, a three-dimensional system of homogeneous partial differential stability equations is derived within the framework of the spatial theory of elasticity. The reduction of a three-dimensional system to a one-dimensional one is carried out along the generatrix and in the circular direction - by expanding the components of stresses and displacements into double trigonometric series when applying the procedure of the Bubnov-Galorkin method, as well as taking into account the periodicity of the resolving functions. An algorithm has been developed, implemented in the form of application software packages for PCs. In it, in a single computational process using the numerical method of discrete orthogonalization in the direction normal to the middle surface of the shell, the establishment of the parameters of the subcritical stress-strain state and the solution on this basis of stability problems for non-thin anisotropic cylindrical shells under the influence of torsion are combined. The problem of the influence on the stability of an anisotropic cylindrical non-thin shell of an increase in the number of cross-reinforced layers depending on the angle of rotation of the main directions of elasticity of the material and the direction of application of torque is considered. The obtained results of stability calculations according to the proposed approach were compared with critical torsion loads calculated using an orthotropic model for calculating anisotropic shells. It is shown that for single-layer cylindrical shells the difference between the compared results reaches 69%. An increase in the number of cross-reinforced layers leads to a decrease in this discrepancy, and with seven to eight layers, the difference between the critical loads obtained using the described approach and the orthotropic model is within 5%. This result is consistent with those obtained using classical or refined theories of calculations of both thin and non-thin anisotropic cylindrical shells.

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Section: Statement Of the Problem And Methods Of Solutionmentioning

confidence: 99%

Stability of cylindrical anisotropic composite shells under torsion in a three-dimensional formulation

Trach,

Podvornyi

2023

OMTC

View full text Add to dashboard Cite

show abstract

“…The algorithm for calculating the structure under consideration is based on the application of the discrete-continuous model [2,5], which is developed below for the case of irregular variable shell parameters [9,10,18]. Differential equations of the linear moment theory of shells in partial derivatives describing the state of the shells under asymmetric loading for the case of a change in the thickness of the shell wall only in the meridional direction h = h(s), using the expansions of the external load, internal forces, and displacements in the Fourier series by circular coordinate in the form [2,10,[18][19][20]…”

Section: Algorithm Of Direct Calculation Of Shells Of Rotation With V...mentioning

confidence: 99%

“…Here f A k , f s k , ψ c k , ψ s k are coefficients of such expansions into trigonometric series, respectively, for symmetric and obliquely symmetric component movements, internal forces and loads; ζ, ξ, ϑ 1 , v are components of movements, and Xr, Zr, M 1 r, S * 1 r are internal efforts, respectively; āke , bke are matrices of coefficients of Fourier series expansions of boundary conditions. The purpose and sequence of the components of the vector Ȳk is adopted in accordance with [18].…”

Section: Algorithm Of Direct Calculation Of Shells Of Rotation With V...mentioning

confidence: 99%

“…Since the forces and displacements in the equations of state of the shell in [5,9,18] are related to the local coordinate system related to the normal and tangent to the meridian, the coefficients of the system may have gaps in the case when the meridian of the shell consists of several sections with angular points between them. This leads to the need to construct compatibility equations of deformation of different areas.…”

Section: Algorithm Of Direct Calculation Of Shells Of Rotation With V...mentioning

confidence: 99%

“…are Poisson's ratios and elastic moduli in the meridional and circumferential directions, respectively; r(s) is the radius of a parallel circle; θ(s) is the angle between the normal to the middle surface of the shell and the axis of rotation. The integration of the boundary value problems ( 7), (8) for each of the structural shells is carried out by the orthogonal sweep method [18,19].…”

Section: Algorithm Of Direct Calculation Of Shells Of Rotation With V...mentioning

confidence: 99%

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Parameter optimization decomposition and synthesis algorithm for a bundle of rotation shells connected with a ring frame

Dzyuba,

Safronova,

Sirenko

et al. 2023

Math. Model. Comput.

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The method of weight optimization of a shell structure consisting of a power ring frame connected to it on each side of non-homogeneous shells of rotation with variable wall thickness under the action of a spatially asymmetric load is presented. The construction decomposition algorithm is applied. The optimization of shells is carried out based on the necessary Pontryagin's optimality conditions with phase constraints. Finite-dimensional optimization methods are used to seek the optimal configuration of the ring frame. The synthesis of the construction is carried out by the method of successive approximations. Numerical optimization results are presented

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Influence of Geometric Parameters of Conical Acrylic Portholes on Their Stress–Strain Behaviour

et al. 2022

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Translucent elements in the form of truncated cones, which are made of organic glass, are widely used in the structures of portholes, submersible vessels, space vehicles, pressure chambers, teleboxes and other types of technical equipment. The decisive factor in designing portholes is to ensure the strength of their translucent elements. In order to reduce the weight of portholes and, accordingly, to increase the payload, it is necessary to optimise the geometric parameters of the translucent elements, which include the tapering angle and the ratio of thickness to radius of the smaller base. The paper deals with development of the applied (engineering) method for determining the stress–strain behaviour of the conical translucent elements of portholes made of organic glass under the action of a uniform hydrostatic pressure. Finite-element modelling of the translucent element of the conical porthole is performed, with the calculation of its stress–strain behaviour. External hydrostatic pressure of 10 MPa, absence of loads from the inside and continuous sliding of the translucent element with friction along the conical supporting surface of the porthole metal body are the boundary conditions for the computational model. Full-scale tests of translucent elements of portholes made of organic glass were performed under the action of uniform hydrostatic pressure. Analysis of the influence of geometric characteristics of the portholes on stress–strain behaviour showed that the increase in the tapering angle at the constant relative thickness of the translucent element reduced its axial displacement in all cases. Equivalent stresses acquire minimum values when the tapering angle is in the range from 75° to 105° (when the relative thickness increases, the optimal tapering angle becomes smaller). It is shown that the developed method for determination of the stress–strain behaviour of the conical translucent elements of portholes made of organic glass reflects the real picture of deformation and agrees with the results of full-scale tests. Results of the work allow us to choose the rational parameters of the translucent element for increasing the reliability of portholes through the creation of an effective distribution of stresses and strains in the translucent element, and improving its optical characteristics due to a relatively small deflection in operation.

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Solutions of Static Problems Based on the Refined Model

Cited by 3 publications

References 16 publications

Stability of cylindrical anisotropic composite shells under torsion in a three-dimensional formulation

Stability of cylindrical anisotropic composite shells under torsion in a three-dimensional formulation

Parameter optimization decomposition and synthesis algorithm for a bundle of rotation shells connected with a ring frame

Influence of Geometric Parameters of Conical Acrylic Portholes on Their Stress–Strain Behaviour

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