In the present paper the coupled linear theory of double-porosity viscoelastic materials is considered and the basic boundary value problems (BVPs) of steady vibrations are investigated. Indeed, in the beginning, the systems of equations of motion and steady vibrations are presented. Then, Green’s identities are established and the uniqueness theorems for classical solutions of the BVPs of steady vibrations are proved. The fundamental solution of the system of steady vibration equations is constructed and the basic properties of the potentials (surface and volume) are given. Finally, the existence theorems for classical solutions of the above mentioned BVPs are proved by using the potential method (the boundary integral equations method) and the theory of singular integral equations.

The ponding on an inflated membrane tube is studied. Membrane tubes have the advantage of zero leakage and ease of transportation and set-up. A novel related problem is the membrane trough which can be used to contain water and does not need anchoring. These problems depend on two non-dimensional parameters which characterize membrane tension and pressure. Perturbation solutions to second order are found for shallow ponding, and compare well with those of exact numerical integration. Tables for the pertinent parameters are constructed and cross section geometries are found. This research illustrates the interaction of membrane structure, pressure load, and hydrostatics.

The paper presents the local linear stability analysis of the double annular jets. The calculations show that the first absolutely unstable helical mode can be generated in the non-swirling annular jets by the back-flow in the central recirculation zone or sufficiently strong back-flow in the external recirculation zone. The influence of the back-flow magnitude on the frequency, growth rate and eigenfunctions of the first helical mode is discussed. The calculations are completed with an analysis of the influence of the swirl intensity in the internal and external jets on the characteristics of the first absolutely unstable helical mode.

The linear theory of viscoelasticity remains an important field of research like most solids and polymer materials when exposed to a vicious dynamic loading effect. This article introduces a new model for describing the behavior of thermoviscoelastic microbeams considering the effects of temperature change and the longitudinal magnetic field. The governing equations in this model are derived based on the Euler–Bernoulli beam theory, Kelvin–Voigt model of viscosity, the generalized thermoelasticity, and the classical Maxwell equations. The two ends of the microbeam are clamped and subjected to the influence of a laser pulse with a temporal intensity profile. The analytical solutions to the physical fields are evaluated using the Laplace transform and its inversion transforms are performed numerically. The thermo-viscoelastic responses of the microbeam are calculated numerically and investigated graphically. The effect of different parameters such as viscosity, laser intensity, and the magnitude of the magnetic field are studied in detail.

The main aim of this paper is to derive formulas for the slowness of Stoneley waves traveling along the sliding interface of two isotropic elastic half-spaces. These formulas have been obtained by employing the complex function method. From the derivation of them, it is shown that if a Stoneley wave exists, it is unique. Based on the obtained formulas, it is proved that a Stoneley wave is always possible for two isotropic elastic half-spaces with the same bulk wave velocities. This result leads to the fact that a Stoneley wave is always possible for two elastic half-spaces satisfying the Wiechert condition, a condition that plays an important role in acoustic analyses. The obtained formulas are of theoretical interest and they will be useful in practical applications, especially in nondestructive evaluations.

The presence of an edge dislocation in a surface of a two-dimensional precipitate of square shape embedded in a semi-infinite matrix has been discussed when the precipitate is submitted to misfit strain due to the lattice mismatch between the two phases. Considering any orientation of the precipitate relative to the matrix free-surface, the total force applying on the dislocation has been analytically calculated and its equilibrium position has been determined. The conjugated effects of the precipitate misorientation, of the lattice mismatch and of the precipitate/matrix distance have been finally characterized. A shifting effect on this equilibrium position has been analyzed.

Results of numerical calculations of reinforced concrete (RC) beams are presented. Based on experimental results on longitudinally reinforced specimens of different sizes and shapes are investigated. Four different continuum constitutive laws with isotropic softening are used: one defined within continuum damage mechanics, an elasto-plastic with the Rankine criterion in tension and the Drucker–Prager criterion in compression, a formulation coupling elasto-plasticity and damage mechanics and the concrete damaged plasticity (CDP) model implemented in Abaqus. In a softening regime, a non-local theory of integral format is applied to the first three constitutive laws. A fracture energy approach is utilised in CDP model. An ability to reproduce different failure mechanisms observed in experiments for each constitutive model is analysed. A comparison of force-displacement curves and crack patterns between numerical and experimental outcomes is performed.

As a combination of the traditional finite element method and boundary element method, the n-sided polygonal hybrid finite element method with fundamental solution kernels, named as HFS-FEM, is thoroughly studied in this work for two-dimensional heat conduction in fully anisotropic media. In this approach, the unknown temperature field within the polygon is represented by the linear combination of anisotropic fundamental solutions of problem to achieve the local satisfaction of the related governing equations, but not the specific boundary conditions and the continuity conditions across the element boundary. To tackle such a shortcoming, the frame temperature field is independently defined on the entire boundary of the polygonal element by means of the conventional one-dimensional shape function interpolation. Subsequently, by the hybrid functional with the assumed intra- and inter-element temperature fields, the stiffness equation can be obtained including the line integrals along the element boundary only, whose dimension is reduced by one compared to the domain integrals in the traditional finite elements. This means that the higher computing efficiency is expected. Moreover, any shaped polygonal elements can be constructed in a unified form with the same fundamental solution kernels, including convex and non-convex polygonal elements, to provide greater flexibility in meshing effort for complex geometries. Besides, the element boundary integrals endow the method higher versatility with a non-conforming mesh in the pre-processing stage of the analysis over the traditional FEM. No modification to the HFS-FEM formulation is needed for the non-conforming mesh and the element containing hanging nodes is treated normally as the one with more nodes. Finally, the accuracy, convergence, computing efficiency, stability of non-convex element, and straightforward treatment of non-conforming discretization are discussed for the present n-sided polygonal hybrid finite elements by a few applications in the context of anisotropic heat conduction.

It is shown, using analytical methodologies, that the velocity field blow-up suffered by vertically ascending acoustic waves in an isothermal atmosphere can be eliminated via the introduction of fine particles. Assuming the inhomogeneous generalization of the particle-laden flow model known as the (linearized) Marble–Thompson model-1, it is established that bounded, exponentially decreasing, shock amplitudes can be obtained provided the mass fraction of particles exceeds a critical value, for which an exact expression is derived. Lastly, supporting numerical results are presented, special cases are discussed, and possible follow-on studies are noted.

Modeling of anisotropic behavior as well as hardening behavior based on micromechanical quantities in combination with a spectral solver is the focus of this study. A deep drawing steel as well as two different aluminum alloys are investigated. Prediction capabilities of the proposed modeling strategy are discussed and the benefits of the micromechanical model are highlighted. Further, a comparison of the crystal plasticity (CP) results with the well established macroscopic model YLD2000-2d underlines the importance of the CP as a complementary modeling technique to the macroscopic modeling. Both models – the microscopic as well as the macroscopic – are validated on experimental data mainly gained from uniaxial and biaxial tests. In the second part of this study, strong inhomogeneous microstructures are investigated from a modeling point of view. For this purpose, a Hall–Petch phenomenological model is implemented in the CP open-source code DAMASK to take the grain size effects into account. Appropriate combinations of the grain sizes in a bimodal microstructure are presented in order to increase the strength as well as ductility of a generic aluminium alloy. The proposed numerical strategy of coupling the CP and efficient FFT-based spectral solver supports the development of new materials in an optimal way.