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In the present study, elastic body wave propagation in fluid-saturated porous media is investigated, and the analytical model is solved in terms of the model of soil mechanics. The potential function expressions of elastic body waves in fluid-saturated porous media with different permeability (i.e., finite, zero, and infinity) are derived by using potential functions of solid- and liquid-phase displacements. Then, the elastic wave dispersion equations are obtained by using the complex forms of the plane harmonic wave. Furthermore, in the case of finite, zero, and infinite permeability, the plane wave solutions of the elastic waves are derived and the analytical formulations of propagation velocities and attenuation coefficients are calculated. Finally, numerical examples are carried out to analyze the dispersion and attenuation characteristics of three waves (fast compressional wave P1, low compressional wave P2, and shear wave S) in two-phase media. In addition, the effects of various properties (i.e., dynamic permeability coefficient, dissipation coefficient, porosity, and Poisson ratio) on the propagation characteristics of three waves are studied numerically. This study is of value to the wave propagation phenomenon as well as other related disciplines.

In the framework of 2D-elasticity, an equilibrium problem for an inhomogeneous body with a curvilinear inclusion located strictly inside the body is considered. The elastic properties of the inclusion are assumed to depend on a small positive parameter δ characterizing its width and are assumed to be proportional to δ−1. Moreover, it is supposed that the inclusion has a curvilinear rough boundary. Relying on the variational formulation of the equilibrium problem, we perform the asymptotic analysis, as δ tends to zero. As a result, a variational model of an elastic body containing a thin curvilinear rod is constructed. Numerical calculations give a relative error between the initial and limit problems depending on δ.

This paper presents an innovative procedure for the stability assessment of masonry domes, aiming at simplifying the modelling and the computational stages of structural analysis. It exploits a macroscopic approach to discretise masonry, specifically using elastic bodies linked by nonlinear interfaces. The latter are made by axial and, when needed, tangential trusses—in turn characterised by an elastic perfectly plastic/brittle behaviour—which constitute the joints connecting homogenised elastic macroblocks. The objective is—by employing low-cost commercial Finite Element software—to predict the behaviour of a masonry curved structure up to failure, maintaining the computational complexity low and the approach accessible to a common user. The process enables not only the quantification of damage at failure but also the tracking of its evolution within the structure, by examining axial forces found in the trusses at each load step. The method allows the modelling of the response of any kind of masonry structure under imposed loads or displacements. Its efficacy is proven on a paradigmatic dome (Global Vipassana Pagoda, Mumbai, India) by comparing the results with limit analysis precedent studies. Finally, the major reliability of a 3D approach is demonstrated.

The paper addresses the analysis of a boundary value problem with an unknown contact area that describes equilibrium of two-dimensional elastic bodies with a thin weakly curved junction. It is assumed that the junction exfoliates from the elastic bodies to form interfacial cracks. Nonlinear boundary conditions in the form of inequalities are set on the crack faces and exclude the mutual penetration of the edges. The unique solvability of the boundary value problem is established. The analysis of passages to the limit as the junction stiffness parameter tends to infinity and to zero is carried out, and limit models are investigated.

In the paper, we analyze problems of elasticity tensor identification for an elastic body with incorporated thin elastic and rigid inclusions in a non-coercive case. The inclusions are assumed to be delaminated from the surrounding elastic body, thus forming interfacial cracks. We consider inequality-type boundary conditions at the crack faces with unknown set of a contact to provide a mutual non-penetration between the crack faces. The considered problems are characterized by unknown displacement field and elasticity tensor. A formulation of identification problems includes an additional information, which can be found from a measurement. A solution existence of these problems is proved.

Purpose This paper aims to propose a method for manufacturing multi-material monolithic structures with flexible materials to construct the elastic body by using a dual-nozzle three-dimensional printer to develop a piezoelectric (PZT)-driven micropositioning stage with three degrees of freedom (3-DOF) and flexure hinges. Design/methodology/approach Polylactic acid (PLA) and nylon were used for the lever structure’s frame and flexure hinge, respectively. Additionally, the stage consisted of three PZT actuators for fine movement in the nanometer scale in 3-DOF (x, y and θ-directions). For the design of the stage, the kinematic analysis model and the finite element method (FEM) analysis was undertaken for comparing between PLA with nylon (multi-material), PLA (single material) and aluminum (conventional-material). In addition, two verification experiments were implemented for the fabricated prototype stage. First, to evaluate various assessments (lever ratio, hysteresis, coupling error and resolution), a measurement is carried out using the three capacitive sensors. Then, a two-camera-vision measurement experiment was performed to verify the displacement and lever ratio over the full-scale working range of the fabricated positioning stage, and the results from the experimentation and the FEM analysis were compared. Findings The authors confirmed enhancements in the properties of the lever structure frame, which requires stiffness and of the hinge, which requires flexibility for elastic deformation. Comparing FEM analysis and experimental results, although the performance as shown by experimental results was lower: the maximum difference being 3.4% within the end-point working range; this difference was sufficient to be a plausible alternative for the aluminum-based stage. Originality/value Multi-material monolithic-structure fabrication has an effective advantage in improving the performance of the stage, by using a combination of materials capable of reinforcing the desired characteristics in the necessary parts. It was verified that the fabricated stage can substitute the aluminum-based stage and can achieve a higher performance than single-material stages. Thus, precise-positioning stages can be manufactured in many kinds of structures with various properties and contribute to weight reduction and low costs for application equipment.

This paper concerns an equilibrium problem for an an elastic body with a thin rigid inclusion crossing an external boundary of the body at zero angle. The inclusion is assumed to be exfoliated from the surrounding elastic material that provides an interfacial crack. To avoid nonphysical interpenetration of the opposite crack faces, we impose inequality type constraints. Moreover, boundary conditions at the crack faces depend on a positive parameter describing a cohesion. A solution existence of the problem with different conditions on the external boundary is proved. Passages to the limit are analyzed as the damage parameter tends to infinity and to zero. Finally, an optimal control problem with a suitable cost functional is investigated. In this case, a part of the rigid inclusion is located outside of the elastic body, and a control function is a shape of the inclusion.

The article studies a 3D contact problem with Coulomb friction for an elastic body resting on a rigid support. The solution of the quasi-variational formulation of the problem is defined as a fixed point of some mapping that associates the given force of the normal reaction of the support with the value of the normal stress in the contact zone. The fixed point is sought by the method of successive approximations, the convergence of which is proved using modified Lagrange functionals. The results of the numerical solution using finite element modeling and the proximal gradient method are presented.

The article considers the case of plane deformation for the Cowin–Nunziato linear model, which describes the static equilibrium of elastic bodies with voids. The general solution of the system of two-dimensional equations corresponding to this model is represented by any two harmonic functions and the solution of the Helmholtz equation. Based on the general solution and using the method of fundamental solutions, an algorithm is presented that allows one to approximately solve the corresponding boundary value problems. Approximate solutions of various boundary value problems for square domains with circular holes are constructed using this algorithm.

We consider the contact between an elastic body and a deformable foundation. Firstly, we introduce a mathematical model for this phenomenon by means of a normal compliance contact condition associated with a friction law. Then, we propose a variational formulation of the model in a form of a quasi-variational inequality governed by a non-differentiable functional and we briefly discuss its well-possedness. Nextly, we address an optimal control problem related to this model in order to led the displacement field as close as possible to a given target by acting with a localized boundary control. By using some mollifiers of the normal compliance functions, we introduce a regularized model which allows us to establish an optimality condition. Finally, by means of asymptotic analysis tools, we show that the solutions of the regularized optimal control problems converge to a solution of the initial optimal control problem.