Mechanics of Solids

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Stress-strain state of an anisotropic plate with curved cracks and thin rigid inclusions
Mechanics of Solids - Tập 42 - Trang 223-230 - 2007
V. N. Maksimenko, E. G. Podruzhin, P. E. Ryabchikov
We solve the bending problem for an anisotropic plate with flaws like smooth curved nonoverlapping through cracks and rigid inclusions. The problem is solved by the method of Lekhnitskii complex potentials specified as Cauchy type integrals over the flaw contours with an unknown integrand density function. We use the Sokhotskii—Plemelj formulas to reduce the boundary-value problem to a system of s...... hiện toàn bộ
General theory of thin plates on the basis of nonsymmetric theory of elasticity
Mechanics of Solids - Tập 47 - Trang 119-136 - 2012
S. O. Sargsyan
The paper uses the asymptotically justified hypothesis method to construct three different general refined theories of micropolar thin elastic plates, depending on the values of physical dimensionless material parameters, involving: (i) independent displacement and rotation fields, (ii) constrained rotation, and (iii) low shear stiffness. All angular shear deformations are taken into account.
Orientation and Kinematics of Rotation: Quaternionic and Four-Dimensional Skew-Symmetric Operators, Equations, and Algorithms
Mechanics of Solids - Tập 57 - Trang 1885-1907 - 2023
Yu. N. Chelnokov
This paper develops a theory of three- and four-dimensional skew-symmetric rotation operators generated by exponential representations of orthogonal operators or their representations using Cayley’s formulas. The generating orthogonal operators involve the direction angle cosine matrix, the quaternionic matrix of Euler’s parameters, and the Hamilton rotation quaternion. Novel matrix and quaternion...... hiện toàn bộ
On paradoxes of the formal approach to determining the eigenvalues of one-dimensional boundary value problems
Mechanics of Solids - Tập 43 - Trang 13-17 - 2008
V. G. Grigoriev
The conventional approach to determining the eigenvalues of a one-dimensional boundary value problem consists in writing out the solution of the differential equation in general form containing indeterminate coefficients and constructing a system of homogeneous linear algebraic equations for these coefficients on the basis of the expressions for the boundary conditions. The eigenvalue is determine...... hiện toàn bộ
High-rate deformation and fracture of steel 09G2S
Mechanics of Solids - Tập 49 - Trang 666-672 - 2015
Vl. Vas. Balandin, Vl. Vl. Balandin, A. M. Bragov, L. A. Igumnov, A. Yu. Konstantinov, A. K. Lomunov
The results of experimental and theoretical studies of steel 09G2S deformation and fracture laws in a wide range of strain rates and temperature variations are given. The dynamic deformation curves and the ultimate characteristics of plasticity in high-rate strain were determined by the Kolsky method in compression, extension, and shear tests. The elastoplastic properties and spall strength were s...... hiện toàn bộ
Interaction of a deformable plate with a stressed half-space
Mechanics of Solids - - 2007
V. M. Alexandrov, В. К. Антонов, Victoria Salamatova
Optimal Traction Control in High-Speed Maneuvering under Dry Friction Conditions
Mechanics of Solids - Tập 58 - Trang 2574-2585 - 2024
S. A. Reshmin
The problem of control of the traction force direction in the course of the motion of an inertial object is considered. The maximum possible value of the traction force is constant and is determined by the maximum dry friction force. Within a finite time range, the problem of bringing an object to a given rectilinear trajectory with simultaneous velocity maximization in the appropriate direction i...... hiện toàn bộ
Periodic Crack Systems in a Transversally Isotropic Solid
Mechanics of Solids - Tập 54 - Trang 533-540 - 2020
T. I. Pozharskii
Three-dimensional problems are studied on periodic chains of elliptic cracks oriented along one of the coordinate axes lying in a plane that is perpendicular to the isotropy planes of a transversely isotropic elastic unbounded body. Using the integral Fourier transform, the problems are reduced to integro-differential equations, whose kernels are presented in the form of series and do not contain ...... hiện toàn bộ
Ill-posed problems in mechanics
Mechanics of Solids - Tập 51 - Trang 538-541 - 2017
V. Ph. Zhuravlev
The notion of ill-posed initial and boundary value problems for partial differential equations was introduced by Hadamard, who also presented the first example of an ill-posed problem for a specific partial differential equation. At the same time, there are numerous examples of ill-posed problems in any field of mechanics. Hadamard and some of his successors believed that any ill-posed problem has...... hiện toàn bộ
Elastic Waves Trapped by a Semi-infinite Strip with Clamped Lateral Sides and a Curved or Broken End
Mechanics of Solids - Tập 58 - Trang 2619-2630 - 2024
S. A. Nazarov
Several geometric conditions for trapping elastic waves by a homogeneous isotropic strip having one or two clamped lateral sides and an arbitrarily curved end face are considered. Resonator shapes that provide any predetermined number of linearly independent trapped modes are found.
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