Nonlinear dynamics of heterogeneous shells Part 1. Statics and dynamics of heterogeneous variable stiffness shells

Awrejcewicz, Jan; Krysko, Anton V.; Mitskevich, S.A.; Zhigalov, Maxim V.; Кrysko, V.А.

doi:10.1016/j.ijnonlinmec.2021.103669

Cited by 10 publications

(4 citation statements)

References 43 publications

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“…Therefore, the main aim of this work to develop a new approach to identifying an arbitrary number of inclusions, geometries and locations in 2D and 3D structures, with high recognition qu Numerical solutions were obtained using the FEM in conjunction with the sl asymptote method. Damage identification is the first step in the investigations o stress-strain state (SSS) and stability of mechanical structures, followed by the stu the SSS and stability of perforated mechanical structures [44] with already-kn inclusion locations, determined by TO.…”

Section: Methodsmentioning

confidence: 99%

“…Numerical solutions were obtained using the FEM in conjunction with the sliding asymptote method. Damage identification is the first step in the investigations of the stress-strain state (SSS) and stability of mechanical structures, followed by the study of the SSS and stability of perforated mechanical structures [44] with already-known inclusion locations, determined by TO.…”

Section: Introductionmentioning

confidence: 99%

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A New Approach to Identifying an Arbitrary Number of Inclusions, Their Geometry and Location in the Structure Using Topological Optimization

et al. 2022

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In the present paper, a new approach to identifying an arbitrary number of inclusions, their geometry and their location in 2D and 3D structures using topological optimization was proposed. The new approach was based on the lack of initial information about the geometry of the inclusions and their location in the structure. The numerical solutions were obtained by the finite element method in combination with the method of moving asymptotes. The convergence of the finite element method at the coincidence of functions and their derivatives was analyzed. Results with an error of no more than 0.5%, i.e., almost exact solutions, were obtained. Identification at impact on the plate temperature and heat flux by solving the inverse problem of heat conduction was produced. Topological optimization for identifying an arbitrary number of inclusions, their geometry and their location in 2D problems was investigated.

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Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A New Approach to Identifying an Arbitrary Number of Inclusions, Their Geometry and Location in the Structure Using Topological Optimization

et al. 2022

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“…The papers [28,29] were devoted to constructing a mathematical model of the statics and dynamics of inhomogeneous shells. In the first part of the article [28], a mathematical model of the statics and dynamics of rectangular shells was developed.…”

Section: Introductionmentioning

confidence: 99%

“…In the first part of the article [28], a mathematical model of the statics and dynamics of rectangular shells was developed. In contrast, the second part of the article [29] reported the nonlinear dynamics and stability of inhomogeneous axisymmetric shells of variable thickness. The mathematical model was based on the Kirchhoff-Love kinematic hypothesis.…”

Section: Introductionmentioning

confidence: 99%

Mathematical modeling of planar physically nonlinear inhomogeneous plates with rectangular cuts in the three-dimensional formulation

et al. 2021

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Mathematical models of planar physically nonlinear inhomogeneous plates with rectangular cuts are constructed based on the three-dimensional (3D) theory of elasticity, the Mises plasticity criterion, and Birger’s method of variable parameters. The theory is developed for arbitrary deformation diagrams, boundary conditions, transverse loads, and material inhomogeneities. Additionally, inhomogeneities in the form of holes of any size and shape are considered. The finite element method is employed to solve the problem, and the convergence of this method is examined. Finally, based on numerical experiments, the influence of various inhomogeneities in the plates on their stress–strain states under the action of static mechanical loads is presented and discussed. Results show that these imbalances existing with the plate’s structure lead to increased plastic deformation.

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Quantification of various reduced order modelling computational methods to study deflection of size-dependent plates

Кrysko

Awrejcewicz

Kalutsky

2023

Computers & Mathematics with Applications

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Nonlinear dynamics of heterogeneous shells Part 1. Statics and dynamics of heterogeneous variable stiffness shells

Cited by 10 publications

References 43 publications

A New Approach to Identifying an Arbitrary Number of Inclusions, Their Geometry and Location in the Structure Using Topological Optimization

A New Approach to Identifying an Arbitrary Number of Inclusions, Their Geometry and Location in the Structure Using Topological Optimization

Mathematical modeling of planar physically nonlinear inhomogeneous plates with rectangular cuts in the three-dimensional formulation

Quantification of various reduced order modelling computational methods to study deflection of size-dependent plates

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