The generalized Wiener–Hopf equations for the elastic wave motion in angular regions

In this work, we introduce a general method to deduce spectral functional equations in elasticity and thus, the generalized Wiener–Hopf equations (GWHEs), for the wave motion in angular regions filled by arbitrary linear homogeneous media and illuminated by sources localized at infinity. The work extends the methodology used in electromagnetic applications and proposes for the first time a complete theory to get the GWHEs in elasticity. In particular, we introduce a vector differential equation of first-order characterized by a matrix that depends on the medium filling the angular region. The functional equations are easily obtained by a projection of the reciprocal vectors of this matrix on the elastic field present on the faces of the angular region. The application of the boundary conditions to the functional equations yields GWHEs for practical problems. This paper extends and applies the general theory to the challenging canonical problem of elastic scattering in angular regions.

Three-dimensional thermo-electro-elastic field in one-dimensional hexagonal piezoelectric quasi-crystal weakened by an elliptical crack

In this paper, an analytical solution is developed for the problem of an infinite 1D hexagonal piezoelectric quasi-crystal medium weakened by an elliptical crack and subjected to mixed loads on the crack surfaces. The mixed loads comprise the phonon pressure, phason pressure, electric displacement, and temperature increment, and the crack surfaces can be electrically permeable or impermeable. Based on a general solution, combined with the generalized potential theory, the steady-state 3D thermo-electro-elastic field variables in the quasi-crystal are obtained in terms of elliptic integral functions and elementary functions. Several important physical quantities on the cracked plane, such as the generalized crack surface displacements, normal stresses, and stress intensity factors, are derived in closed forms. An illustrative numerical calculation verifies the presented analytical solution and shows the distribution of the 3D thermo-electro-elastic field. It is indicated that the influence of the phason field on the result is pronounced, especially for the electric field variables, and the electric permeability of crack surfaces has a significant effect on the electric displacement intensity factor at the crack tip.

Singularly Perturbed Solutions for a Class of Thermoelastic Weakly Coupled Problems

Based on the basic equation of Green Lindsay (G-L) theory, the thermoelastic weak coupling problem under the basic equation is discussed, that is, two thermal relaxation parameters are added to the constitutive equation, the influence of the coupling term on the temperature field and elastic field is considered, and the asymptotic solution of the governing equation is constructed. Firstly, in order to obtain the asymptotic solution, the singularly perturbed expansion method is used.Then,combined with the corresponding boundary conditions, the partial differential equation method is used to solve the external solution and the boundary layer correction term. Secondly, in the case of weak coupling, the uniformly efficient estimation of the remainder of the asymptotic solution is obtained by using Gronwall inequality, so as to obtain the uniformly efficient of the formal asymptotic solution. Finally, the first term of the asymptotic solution is numerically analyzed by using the singularly perturbed numerical method. The present work will be conducive to the analysis of thermoelastic processes and numerical simulation of different materials in the case of weak coupling.

Investigation of the coupling effect of flexoelectricity and ferroelasticity on energy storage efficiency of relaxor ferroelectrics

The Ginzburg–Landau theory and dipole defect model have been employed to investigate the flexoelectric and ferroelastic effects on the ferroelectric and energy storage properties of relaxor ferroelectrics (RFs). The results obtained show that due to the existence of polar nanoregions (PNRs) in RFs, the elastic field of the material, which is induced by both the flexoelectric and ferroelastic effects, leads to the increase of the domain switching energy and coercive field and the decrease of the energy storage efficiency. In contrast, the short-range electric field induced by the dipole defects enhances the energy storage efficiency of the material by enhancing the material’s relaxor behavior. Hence, the energy storage efficiency of RFs can be effectively functionalized by modulating the composition ratio and the electric field of the RF materials.

Seismic Design and Performances of Frame Structures Connected to a Strongback System and Equipped with Different Configurations of Supplemental Viscous Dampers

The paper investigates the dynamic behavior of structural systems obtained by connecting a moment-resisting frame structure with a vertical rigid truss pinned at the base, known in literature as “strongback,” and equipped with added fluid-viscous dampers. The strongback, designed in order to remain in the elastic field under strong seismic ground motion, acts as a mast by imposing to the structure a linear lateral deformed shape. By regularizing the lateral drift profile of the structure, the strongback limits undesired effects such as weak-storey mechanisms, damage concentration and residual drifts. In addition, when supplemental dampers are inserted in the structure, a considerable amount of energy can be dissipated, thus reducing the peak seismic response. The aim of the work is twofold: i) to provide analytical formulations for the preliminary design of added dampers based on the Generalized Single Degree Of Freedom (GSDOF) concept, and ii) to evaluate the increase in energy dissipation capabilities for selected dampers configurations thanks to the presence of the strongback. The formulas are developed for different configurations of added viscous dampers: dampers inserted within the frame between all or selected consecutive storeys (inter-storey placement) and dampers located at the base of the strongback to realize a rigid “dissipative tower.” The effectiveness of the dampers configurations is evaluated through dynamic time-history analyses.

Numerical study on butterfly wings around inclusion based on damage evolution and semi-analytical method

Butterfly wings are closely related to the premature failure of rolling element bearings. In this study, butterfly formation is investigated using the developed semi-analytical three-dimensional (3D) contact model incorporating inclusion and material property degradation. The 3D elastic field introduced by inhomogeneous inclusion is solved by using numerical approaches, which include the equivalent inclusion method (EIM) and the conjugate gradient method (CGM). The accumulation of fatigue damage surrounding inclusions is described using continuum damage mechanics. The coupling between the development of the damaged zone and the stress field is considered. The effects of the inclusion properties on the contact status and butterfly formation are discussed in detail. The model provides a potential method for quantifying material defects and fatigue behavior in terms of the deterioration of material properties.

Calculation of the Collapsing Critical Load of a Translating Cam Mechanism and Roller Translating Follower Actuating an Elevator

The above-ground parking lot above Dâmbovița river has stemmed from the need to cover the lack of parking lots in Bucharest. The parking lot may be serviced, in case of emergency, by auxiliary elevators that are operated by mechanisms provided with translating cams and roller translating followers. In this paper, a calculation of the collapsing critical load shall be performed. One shall also analyze here the rod model and the model with several rods of the mechanism provided with a translating cam and roller translating follower. In order for the rods to resist collapsing, one must be found in the elastic field, thus verifying Euler’s formula.

Modeling of an elastic field scattered by an interface defect

The problem of the shear-wave (SH-wave) diffraction from the semi-infinite interface defect in the rigid junction of the elastic layer and the half-space is solved. The defect is modeled by the impedance surface. The dependences of the scattered displacement field, reflection and transmission coefficients on the structure parameters are presented in analytical form. The examples of numerical modeling of field characteristics are provided.