Calculation of a multilayer orthotropic shallow shell by the method of finite elements

Rasskazov, A. O.

doi:10.1007/bf00883684

Cited by 2 publications

(6 citation statements)

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“…The element constructed in [12] is a refined version of the Reddy element. Due to the character of approximation, the elements given in [10] and [12] are very close. However, in [10], the physical-mechanical features of the structure of the I Submitted to the 10th International Conference on Mechanics of Composite Materials (Riga, April 20-23, 1998 layers are taken into account while formulating the approximation of displacements over the thickness of the plate, which is characteristic of the elements constructed according to the approach described in [14].…”

Section: Displacements and Transverse Normal Stresses In Sandwich Plamentioning

confidence: 90%

“…Due to the character of approximation, the elements given in [10] and [12] are very close. However, in [10], the physical-mechanical features of the structure of the I Submitted to the 10th International Conference on Mechanics of Composite Materials (Riga, April 20-23, 1998 layers are taken into account while formulating the approximation of displacements over the thickness of the plate, which is characteristic of the elements constructed according to the approach described in [14]. The element developed further in [16] and based on the theory of [14] took into account compression from a transverse load [16], which is important for calculating thick plates with the filler compliant in the transverse direction.…”

Section: Displacements and Transverse Normal Stresses In Sandwich Plamentioning

confidence: 90%

“…It can be seen that the model proposed here yields more accurate results in calculating plates highly compliant to shear, as compared to the model in [10]. The possibility of using the studied finite element for calculating transversely strongly compressed plates can be seen in the example of the solution presented in [20].…”

Section: +21mentioning

confidence: 97%

“…Hence, the finite element described in this study is more accurate in calculating plates highly compliant to shear and transverse compression, as compared to the known elements [10][11][12]16] where the order of the resolving system is also independent of the number of layers.…”

Section: +21mentioning

confidence: 98%

“…Here, the order of the resolving system is independent of the number of layers. The elements can in turn be divided into subgroups, namely those based on the TimoshenkouReissner--Mindlin theory and allowing for the first-order shear [6][7][8][9], ~d those taking into account the higher-order shears [10][11][12]. The element discussed in [10] is based on the model described in [13] and developed from the Ambartsumyan theory [14].…”

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confidence: 99%

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Finite element construction for simulating delamination of sandwich composite plates and masses

Marchuk¹

1998

Mech Compos Mater

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Due to their unique properties, laminated composites are widely used in various fields of technology and civil engineering. The finite element method (FEM) is most convenient for calculating ]sminated plates and shells (see, e.g., reviews [1][2][3]).Finite elements may be divided into two groups according to the displacement approximation over the thickness of the structure. The first group (discrete structural approximation) includes elements whose displacements are approximated for each layer separately [4,5] and the order of the system of resolving equations depends on the number of layers. The second group (continuous structural approxlmRtion) comprises elements whose distribution of displacements across the thickness of the structure is assigned for the entire stack as a whole. Here, the order of the resolving system is independent of the number of layers. The elements can in turn be divided into subgroups, namely those based on the TimoshenkouReissner--Mindlin theory and allowing for the first-order shear [6][7][8][9], ~d those taking into account the higher-order shears [10][11][12]. The element discussed in [10] is based on the model described in [13] and developed from the Ambartsumyan theory [14]. The theoretical basis for constructing the Reddy element [11] is given in [15]. The element constructed in [12] is a refined version of the Reddy element. Due to the character of approximation, the elements given in [10] and [12] are very close. However, in [10], the physical-mechanical features of the structure of the

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Section: Displacements and Transverse Normal Stresses In Sandwich Plamentioning

confidence: 90%

Section: Displacements and Transverse Normal Stresses In Sandwich Plamentioning

confidence: 90%

Section: +21mentioning

confidence: 97%

Section: +21mentioning

confidence: 98%

mentioning

confidence: 99%

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Finite element construction for simulating delamination of sandwich composite plates and masses

Marchuk¹

1998

Mech Compos Mater

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Solving problems of thermoviscoelastoplastic and continuous fracture of prismatic bodies

et al. 2009

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A procedure of solving problems of thermoviscoelastoplasticity and continuous fracture of prismatic bodies based on the semianalytic finite-element method is developed and implemented Keywords: thermoviscoelastoplasticity, continuous fracture, semi-analytic finite-element method, prismatic body, spatial problemsIntroduction. The thermoviscoelastoplastic deformation of three-dimensional bodies has to be considered in a great many applied problems [16][17][18][19][20], which should be solved numerically. The finite-element method (FEM) is widely used in scientific and engineering numerical simulation and applied to constantly expanding range of objects and processes. Despite the high efficiency of modern computers, it is of importance to develop modifications of the FEM to be applied to a wide class of objects with specific shape, which makes it possible to optimize the structure of the governing equations and to develop efficient algorithms for solving systems of FEM equations. One of such modifications of the FEM is the semianalytic finite-element method (SFEM), which is currently used to solve a wide range of problems. For example, the application of the SFEM to elastic, elastoplastic, creep, contact, and fracture problems is discussed in [1, 2, 14, 15, etc.].One of the applications of the problem considered here is determining the life of critical elements of power equipment such as turbine blades. Methods for solving spatial creep problems are described in [4, 7, 12, etc.]. In [4,12], the creep of a blade was modeled regardless of its damage. Moreover, these and other studies disregard the facts that a continuous fracture zone may occur and develop and that a crack may form.A method for modeling creep and continuous fracture zones in prismatic bodies was developed in [15]. This method was then used to determine the life of a gas turbine blade taking into account continuous fracture. It was shown that a continuous fracture zone is a stress concentrator with instantaneous plastic strains around. Moreover, blades operate in a stationary inhomogeneous temperature field, which induces thermal strains. These factors give rise to additional stress components, which were neglected in [15]. In [1], it was demonstrated that insignificant changes in the stress-strain state (SSS) have a significant effect on the creep life.To improve the efficiency of the problem-solving method, it is necessary to use finite elements that would allow us to obtain exact solutions based on finite-element models of minimum dimension and efficient algorithms for iterative solution of systems of SFEM equations.Thus, the objective of the present paper is to develop an efficient procedure based on the SFEM for solving problems of thermoviscoelastoplasticity and continuous fracture for prismatic bodies, including derivation of governing equations for new finite elements that account for the variation of the metric tensor in the cross section, to develop efficient algorithms for iterative solution of systems of SFEM equations, and to analyze the i...

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Calculation of a multilayer orthotropic shallow shell by the method of finite elements

Cited by 2 publications

References 1 publication

Finite element construction for simulating delamination of sandwich composite plates and masses

Finite element construction for simulating delamination of sandwich composite plates and masses

Solving problems of thermoviscoelastoplastic and continuous fracture of prismatic bodies

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