Archive of Applied Mechanics

A micro-scale free vibration analysis of composite laminated Timoshenko beam (CLTB) model is developed based on the new modified couple stress theory. In this theory, a new anisotropic constitutive relation is defined for modeling the CLTB. This theory uses rotation–displacement as dependent variable and contains only one material length scale parameter. Hamilton’s principle is employed to derive the governing equations of motion and boundary conditions. This new model can be reduced to composite laminated Bernoulli–Euler beam model of the couple stress theory. An example analysis of free vibration of the cross-ply simply supported CLTB model is adopted, and an explicit expression of analysis solution is given. Additionally, the numerical results show that the present beam models can capture the scale effects of the natural frequencies of the micro-structure.

The application of an interference fit in the assembly process of thin-walled aerospace composite parts is prone to stress stiffness effects, namely the structural stiffness change caused by the inplate-induced stress. Limited applicability has been available in this regard when using the compliant assembly analysis based on the stiffness-invariant assumption, such as the method of influence coefficient. In addition, these materials possess a hierarchical structure that necessitates the use of material uncertainty in the analysis. However, it is costly and complicated to develop uncertainty analysis and modeling calculations at different scales. In this study, a deviation propagation model of the composite structure (DPMoCS) considering the stress-stiffening effect is proposed to improve the analysis efficiency. Based on the geometric nonlinear theory, the factors of interest affecting the stress-stiffening effect in the interference assembly of a thin-walled composite material are investigated, which are the material elastic and stress field. Our simulations are integrated with material uncertainty quantization and propagation across scales to characterize the uncertainty of the factors of interest as well as reduce the computational cost based on the equivalent model. The method is combined with the Monte Carlo-based stochastic finite element method and applied to the assembly analysis of a composite panel subassembly. The results show that consideration of the stress-hardening effect has a significant effect on the DPMoCS and affects the assembly accuracy as the fiber layup angle deviation increases.

In this work, the influences of nonlocal interactions on the growing inclusion are studied which are embedded in an elastic wave metamaterial with local resonators. The nonlocal interactions between main resonators are considered as linear springs connected to the second nearest neighboring ones. In addition, the inclusion is supposed that particle masses change along a straight line. Based on the Wiener–Hopf method, the ratio of the tip to end displacements of the inclusion is derived. Furthermore, the dynamic effective mass and stop band frequency are discussed. Numerical results show that in comparison with the system without nonlocal interactions, the new periodic structure can make the displacement ratio tend to the case of homogeneous lattices for high-speed regions. It indicates that more powerful resistance can be created by nonlocal springs during the inclusion growth.

In this contribution we present a phenomenological mesoscopic thermodynamically consistent model for the description of switching processes in ferroelectric materials that is able to describe the fundamental electromechanical hysteresis effects. The main goal is to develop a representation using the set of independent variables, the strains and the electric field, in a coordinate-invariant setting. This formulation is particularly suitable for the treatment of a variety of complex boundary-value problems (BVP) with regard to the essential boundary conditions. Here we restrict ourselves to transversely isotropic solids. The anisotropic behavior is governed by isotropic tensor functions that depend on a finite set of invariants. Thus the material symmetry requirements are automatically fulfilled.

The use of Sectorial coordinates is unavoidable when studying thin-walled elements with open cross sections. The torsional behavior of this type of elements is governed by some fundamental sectorial properties such as the position of the principal pole, i.e., the shear center, and the warping constant or sectorial moment of inertia. However, and despite being a fundamental concept, the definition of the Principal Sectorial coordinate system has not been clearly presented in the literature, and some errors can be found in the diagrams of sectorial areas in well-known text books. Moreover, the Principal Sectorial coordinate system is used, but the location of the principal origin is usually avoided. In this paper, a compact and alternative procedure to obtain the principal sectorial coordinate system is presented. Authors propose to put aside the traditional definition of Principal Origin and consider instead the value of the sectorial area at an extreme of the contour line. Several examples are developed.

We consider the elastodynamic impact problem involving a one-dimensional finite-thickness piezoelectric flyer traveling at initial velocity $$V_0$$ that collides with (and adheres to) a stationary piezoelectric target of finite thickness backed by a semi-infinite non-piezoelectric elastic half-space. We derive expressions for the stress, velocity, and electric displacement in the target at all times after impact. A combined d’Alembert and Laplace transform method is used to derive new numerically based solutions for this class of transient wave propagation problems. A modified Dubner–Abate–Crump (DAC) algorithm is used to invert the analytical Laplace transform domain solutions to the time domain. Unlike many authors who neglect electromechanical coupling in the initially unstressed region ahead of the shock, we consider this effect, which gives rise to the development of a tensile stress wave within the piezoelectric target ahead of the shock. To solve the problem, we derive a new piezoelectric impact boundary condition and apply it to the problem of a finite quartz (Si $$\text {O}_2$$ ) flyer impacting a lead zirconate titanate (PZT-4) target and find that the solutions obtained using the modified DAC algorithm compare well with those obtained using both a finite-difference time-domain method, and the commercial finite element code, COMSOL multiphysics.