Elastoplastic state of axisymmetrically loaded laminated bodies of revolution made of isotropic and orthotropic materials

Shevchenko, Yu. N.; Piskun, V. V.; Kovalenko, V. A.

doi:10.1007/bf00847326

Int Appl Mech

1992

DOI: 10.1007/bf00847326

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Elastoplastic state of axisymmetrically loaded laminated bodies of revolution made of isotropic and orthotropic materials

Yu. N. Shevchenko¹,

V. V. Piskun²,

V. A. Kovalenko³

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2005

2024

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Cited by 3 publications

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“…The quantities with the superscripts i, j, and k correspond to their values at the nodes of an isolated triangular element with nodes i, j, and k. On each time interval, the numerical solution of the elastoplastic problem is obtained by the iterative method of variable parameters. The convergence criterion for the iterative process is the same as that used to solve quasinonstationary elastoplastic problems [5,7]. Unloading is a linear process.…”

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Elastoplastic Deformation of a Compound Disk under Impulsive Loading

Piskun

2005

Int Appl Mech

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The small elastoplastic deformation theory and the finite-element method are used to analyze the behavior of a compound disk under axisymmetric impulsive loading. Numerical results are presented, which describe the development of plastic deformation, the effect of hardening and the duration of the loading impulse on the oscillatory elastoplastic deformation of the disk Keywords: solid of revolution, theory of plasticity, isotropic material, finite elements, impulsive loading, unloading A method for solving the axisymmetric dynamic problem for isotropic elastoplastic solids of revolution with arbitrary meridional section under impulsive thermomechanical loading was proposed in [11]. The method is based on small elastoplastic deformation theory [1, 2, 8, etc.] and involves the finite-element approximation of unknown displacements in spatial coordinates and finite-difference representation of time derivatives. The nonlinear problem is linearized by the method of variable parameters. In the present paper, this method is extended to compound solids of revolution of finite dimensions. By a compound solid is meant a discretely inhomogeneous solid of revolution whose constituents are solids of revolution. For the entire body and for its parts, there is a common axis of revolution coinciding with the z-axis of a cylindrical coordinate system z, r, ϕ. The constituents of the body are made of dissimilar isotropic materials characterized by different (real) limit σ-ε relationships and are in perfect mechanical contact with each other.1. Solution Method. Let the basic unknowns be the axial (U z (z, r, t)) and radial (U r (z, r, t)) displacements. We will use a triangular ring finite element with linear approximation of the displacement vector to partition the meridional section of the solid into triangles by a technique described in [4]. If the meridional section is approximated by N nodes and M triangles with node numbers i, j, and k, then we have the following recurrent formulas of the explicit scheme for computing the displacements at the time (t + ∆t) in terms of the displacement at the previous times t and (t -∆t):u t t u t u t t t M c u r i r i r i m i m M ii m z ( ) ( ) ( ) ( ) ( ) + = − − − = ∑ ∆ ∆ ∆ 2 2 1 1 [ i ii m r i m M t d u t ( ) ( ) ( ) + = ∑ 1 1

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Elastoplastic Deformation of a Compound Disk under Impulsive Loading

Piskun

2005

Int Appl Mech

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Three-Dimensional Problems of Thermoviscoplasticity: Focus on Ukrainian Research (Review)

Shevchenko

Savchenko

2016

Int Appl Mech

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Nonlinear Deformation of Cylinders from Materials with Different Behavior in Tension and Compression

Galishin,

Sklepus

2024

J. of Mech. Eng.

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A new numerical-analytical method for solving physically nonlinear deformation problems of axisymmetrically loaded cylinders made of materials with different behavior in tension and compression has been developed. To linearize the problem, the uninterrupted parameter continuation method was used. For the variational formulation of the linearized problem, a functional in the Lagrange form, defined on the kinematically possible displacement rates, is constructed. To find the main unknowns of the problem of physically nonlinear cylinder deformation, the Cauchy problem for the system of ordinary differential equations is formulated. The Cauchy problem was solved by the Runge-Kutta-Merson method with automatic step selection. The initial conditions were established by solving the problem of linear elastic deformation. The right-hand sides of the differential equations at fixed values of the load parameter corresponding to the Runge-Kutta-Merson’s scheme are found from the solution of the variational problem for the functional in the Lagrange form. Variational problems are solved using the Ritz method. The test problem for the nonlinear elastic deformation of a thin cylindrical shell is solved. Coincidence of the spatial solution with the shell solution was obtained. Physically nonlinear deformation of a thick-walled cylinder was studied. It is shown that failure to take into account the different behavior of the material under tension and compression leads to significant errors in the calculations of stress-strain state parameters.

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Elastoplastic state of axisymmetrically loaded laminated bodies of revolution made of isotropic and orthotropic materials

Cited by 3 publications

References 0 publications

Elastoplastic Deformation of a Compound Disk under Impulsive Loading

Elastoplastic Deformation of a Compound Disk under Impulsive Loading

Three-Dimensional Problems of Thermoviscoplasticity: Focus on Ukrainian Research (Review)

Nonlinear Deformation of Cylinders from Materials with Different Behavior in Tension and Compression

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