Finite element dynamic analysis of anisotropic elastic solids with voids

Iovane, Gerardo; Наседкин, А. В.

doi:10.1016/j.compstruc.2008.04.017

Cited by 20 publications

(6 citation statements)

References 11 publications

(18 reference statements)

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“…In this case, the boundaries (10) on the lower and upper surfaces of the beam should be used, instead of (12) that was used in Cowin and Nunziato [1]. This solution is completely similar to (17)- (24), but instead of expressions (22) and (24), the following expressions should be used:…”

Section: Analytical Solution Of the Beam Pure Bending Problem With Sumentioning

confidence: 99%

“…If there is no coupling in the media (N=0), the effective flexural modulus is equal to the material Young's modulus. In equation 31, there is an explicit relation between thickness and scale parameter h=' (see (22)- (26)). Thus, an analytical solution predicts the scale effects.…”

Section: Analytical Solution For the Pure Bending Testmentioning

confidence: 99%

“…At first, the numerical solutions of the two-dimensional (2D) static and dynamic problems in the frame of the void elasticity theory were presented by Iovane and Nasedkin [21, 22]. The authors provided the finite-element (FE) simulations using a solver with direct estimation algorithms.…”

Section: Introductionmentioning

confidence: 99%

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Bending problems in the theory of elastic materials with voids and surface effects

Lurie

Solyaev

Волков

et al. 2017

Mathematics and Mechanics of Solids

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In the present study, a comparison of pure, three-point, four-point and cantilever beam bending problems in the frame of the theory of elastic materials with voids (micro-dilatational elasticity) has been provided via analytical modelling and three-dimensional finite-element analysis. We consider the extended variant of the theory with surface effects using a variational approach. At first, we compare the known approximate semi-inverse analytical solution of the pure bending problem with a corresponding three-dimensional finite-element solution in the frame of micro-dilatational theory. It is demonstrated that in the numerical solution – unlike the analytical one – all boundary conditions are satisfied accurately, and there exist distortions of the cross-sections and lateral faces of the beam. The generalized analytical solution of the beam pure bending problem with surface effects is also established and compared with numerical simulations. The effective elastic properties of the beam with micro-dilatations are introduced by comparing its displacements and corresponding classical beam displacements. The influence of scale, coupling and surface parameters on the effective elastic moduli in different bending and simple tension tests is studied. It is shown that all considered types of bending experiments provide the determination of close values of the effective flexural modulus of the beams with different thickness. This means that it is possible to use any bending test with beams of different thickness for reliable identification of the material constants of the theory. It is also possible to use the simple analytical expression for an effective flexural modulus that follows from the analytical solution of the pure bending problem. It is also shown that stiffness of the beam with micro-dilatation in any bending tests should always be higher as compared with the stiffness of such a beam in simple tension. For thin beams, there are no scale effects, and its effective flexural modulus is equal to the material’s Young’s modulus without micro-dilatation. Possible rise of the negative size effects in the model with surface effects is also discussed.

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Section: Analytical Solution Of the Beam Pure Bending Problem With Sumentioning

confidence: 99%

Section: Analytical Solution For the Pure Bending Testmentioning

confidence: 99%

See 1 more Smart Citation

Bending problems in the theory of elastic materials with voids and surface effects

Lurie

Solyaev

Волков

et al. 2017

Mathematics and Mechanics of Solids

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“…Ряд работ посвящен численному исследованию пористых материалов. Для получения численных решений статических задач для среды с порами использовался метод конечных элементов [23,24]. В [25] методом Петрова -Галеркина исследовано влияние пористости на напряжения (а meshless local Petrov -Galerkin).…”

Section: Introductionunclassified

Relative Pore Volume Under Indentation of Porous Materials

Zelentsov

Zagrebneva

Lapina

et al. 2021

PSP

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Investigation of the function of the relative volume of pores under the load action is carried out on the base of the solution of the static contact problem of the indentation of a layer made of a material with voids or unfilled pores. A rigid strip indenter with a flat base is pressed into a porous layer that is adhered to a non-deformable base along the lower boundary. The formulated 3D problem of the indentation of a porous layer is reduced to solving the plane contact problem of the indentation of a porous strip. The plane contact problem is reduced to solving an integral equation for unknown contact stresses, the solution of which is constructed by the method of successive approximations in the form of an asymptotic expansion in the dimensionless parameter of the problem. The obtained contact stresses and the force acting on the indenter made it possible to study the influence of the nonclassical moduli of the layer porous material (the connectivity modulus and pore rigidity modulus) on the main contact characteristics and on the distribution of the function of the relative pore volume. The connectivity modulus increase leads to an increase in the compliance of the layer porous material, the pore rigidity modulus increase leads to an increase in the rigidity of the layer porous material. The maximum value of the distribution function of the relative pore volume in the porous material of the layer is achieved under the indenter base centre, regardless of the change in the porous material non-classical moduli.

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“…9 Ibrahimbegovic and Mamouri 10 used the finite element implementation of the internal constraints in a three-dimensional geometrically exact beam model which can be formulated as holonomic constraint relationships. Iovane and Nasedkin 11 proposed a set of new finite element schemes for finding numerical solutions of transient, harmonic, modal and static problems in the context of elastic media with voids. Ambarisha and Parker 12 examined the complex, nonlinear dynamic behavior of spur planetary gears using both the lumped-parameter model and finite element model, but the FEM is used just for calculating the deformations of gears, and the dynamics of gear system is simulated only through the lumped-parameter model.…”

Section: Introductionmentioning

confidence: 99%

Dynamic modeling of flexible multibody system using a meshing method

Zhao

Chu

2013

Proceedings of the Institution of Mechanical Engineers, Part C:

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Multi-rigid-body system dynamics can be used to investigate the dynamics of a mechanical system of rigid bodies while the finite element method is often utilized to model the quasi-static elastic deformations of an elastic structure. However, neither of these two methods can resolve the real dynamics of a mechanical system when both rigid displacements and elastic deformations coexist. Therefore, this article proposes a meshing method to simulate the mechanical system with uniform mass point movements. To split the specified solid structure into a set of regularly distributed dynamic units, one can assume that the mass density of the structure is evenly distributed within the whole concrete volume and the elasticity and damping of the material are isotropic. Then the whole solid structure of each component can be divided into a number of tetrahedrons the vertexes of which are the points with the mass parameters. The original distances between every pair of adjacent points are supposed to be identical, and the stiffness and the damping coefficients are introduced to formulate the internal and external dynamics of the adjacent mass points. To illustrate the correction and effectiveness of the method, the dynamics problems of a number of regular elastic bodies are investigated with large rigid displacements accompanying elastic deformations. Computer simulations demonstrate that this method is especially useful for real mechanical systems where the rigid displacements and elastic deformations coexist.

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Finite element dynamic analysis of anisotropic elastic solids with voids

Cited by 20 publications

References 11 publications

Bending problems in the theory of elastic materials with voids and surface effects

Bending problems in the theory of elastic materials with voids and surface effects

Relative Pore Volume Under Indentation of Porous Materials

Dynamic modeling of flexible multibody system using a meshing method

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