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Solving of Stress State Problems of Anisotropic Thick Noncircular Cylindrical Shells with Different Nonhomogeneous Structures Based on Discrete Continual Approach
In this study, we introduce a novel approach utilizing discrete continual numerical methods to tackle the strain state problem of anisotropic...
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Fatigue Endurance of Thin-Walled Cylindrical Shells Under Biaxial Combined Loading
The problem of determining the number of cycles to failure of thin-walled cylindrical shells due to multicycle fatigue under combined uniaxial...
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Numerical Analysis of Free Vibration Frequencies of Hexagonal Plate
Free vibrations of the isotropic hexagonal plates of the different thicknesses with the free edges are considered based on two different approaches....
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Dynamics of Three-Layer Spherical Shells with Heterogeneous Filler Under Nonstationary Loads
The dynamics of a three-layer spherical shell with a discrete-symmetric lightweight, rib-reinforced aggregate under nonstationary loads were studied....
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Solving Incorrect Problems of the Elasticity Theory
The possibilities of effective research and calculation of mathematical models described by problems with a unique solution on the subspace are...
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Topology Optimization of Adhesively Bonded Double Lap Joint
In this paper, a one-dimensional mathematical model of stress state is proposed for a symmetrical double-shear adhesive joint with doublers having...
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Longitudinal Shear of Bimaterials with Interphase Thin Physically Nonlinear Layered Functional-Gradient Inhomogeneities
An analytical–numerical method for solving the class of problems of determining mechanical fields in composite structures with interfacial...
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Asymptotic Behavior of Forced Vibrations of Layered Plates
This article delves into dynamic three-dimensional elasticity problems specifically tailored for layered plates. In contrast to classical and...
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Two-Parametric Analysis of a Semi-Infinite Three-Layered High-Contrast Elastic Strip Under Antiplane Shear Deformation
Antiplane shear of a symmetric three-layered elastic semi-strip under the self-equilibrated edge load is studied. The arbitrary ratios of thickness...
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Methods of Numerical Solution of Problems of Thermo-Plasticity Taking into Account the Stress Mode
This study presents advanced numerical methods for analyzing the elastic–plastic stress–strain behavior of compound bodies subjected to thermo-force...
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Numerical Analysis of Contact Between Elastic Bodies in the Presence of Thin Coating and Nonlinear Winkler Surface Layers
We consider the problem of unilateral contact through a nonlinear Winkler surface layer of a massive elastic body and a composite body consisting of...
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Numerical Methods for Fractional PDEs
Numerical approaches for the computation of fractional derivatives on the whole real line (also called the fractional Laplacian) are discussed....
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Traveling Waves in Fractional Models
Fractional models of the Korteweg-de Vries (KdV) type are discussed in the context of propagation of one-dimensional traveling waves in nonlocal...
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Fractional Models in Biology and Medicine
Fractional models have a long history in areas such as hydrology, heterogeneous media, animal movement and explorations of anomalous diffusion, to...
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Asymptotic Formulas for the Bloch Eigenvalues and Bloch Functions
In this chapter, we construct a perturbation theory for the multidimensional Schrödinger operatorSchrödinger operator with a periodic potential. This...
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From One-Dimensional to Multidimensional
In this chapter, we construct a perturbation theory for two and three dimensional Schrödinger operatorsSchrödinger operator with a periodic...
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Constructive Determination of the Spectral Invariants
In this chapter describes the constructive determinationConstructive determination of the spectral invariantsSpectral invariants explicitly expressed...
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Preliminary Facts
In this chapter, we present some definitions and statements from the points of view of both physicists and mathematicians to be used in the next...
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Symmetry Breaking in Fractional Nonlinear Schrödinger and Soliton Dynamics in Complex Ginzburg-Landau Models
In this chapter we review some recent results for fractional nonlinear Schrödinger (FNLS) and fractional complex Ginzburg-Landau (FCGL) models. In...
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Fractional Dissipative PDEs
In this chapter we provide an introduction to fractional dissipative partial differential equations (PDEs) with a focus on trying to understand their...