International Journal of Applied Mechanics

Residual stress plays an important role in the mechanical performance of engineering structures. In this paper, the indentation of pre-stressed strain hardening materials by a rigid sphere is simulated through the finite element method. It is shown that the mean contact pressure in the post-yield regime keeps continuously increasing with the indentation proceeding. Compared to the case without residual stress, compressive residual stress tends to increase the mean contact pressure at a given indentation depth, while tensile stress has an inverse effect. To quantitatively indicate the influence of residual stress, a nominal contact pressure is defined, which obtains its maximum value at a critical depth. The dependences of the maximum nominal pressure and the critical indentation depth on the residual stress and the material properties are determined explicitly through large numbers of simulations. Inspired by the nominal pressure deviation stemmed from residual stress, a new approach is proposed for measuring residual stress through spherical indentation tests.

In this paper, we present a hybrid immersed boundary method (HIBM) for the simulation of two- and three-dimensional compressible viscous flows around stationary and moving obstacles. The proposed approach combines the compressible boundary condition-enforced IBM proposed by Qiu et al. and the Brinkman penalization methods. The boundary condition-enforced IBM uses a fractional step approach alongside a Dirac delta function to satisfy the boundary conditions on the body surface. Although this method works properly in subsonic regimes, it cannot correctly simulate the wake region for a supersonic flow. On the other hand, the penalization method considers the body as a porous media with a low permeability that forces the velocity and energy inside the body to converge to the body velocity and energy. However, unlike the boundary condition-enforced IBM, the streamlines penetrate the body. In the present approach, the positive features of the above-mentioned methods were included and their drawbacks were excluded. The proposed approach was applied using the finite volume method and an E-CUSP scheme. The performance of the proposed method was numerically evaluated in simulating compressible fluid flow around both stationary and moving boundaries, showing a close agreement with other numerical and experimental data available in the literature. Further, the effects of geometry, Reynolds, and Mach numbers were investigated on the supersonic flow field around elliptical cylinders of various aspect ratios. The results revealed that increasing the aspect ratio led to an increase in the shock standoff distance, recirculation zone, and drag coefficient.

Numerical analysis of wave propagation in composite structures needs large-scale computation which is not feasible in practice. This paper investigates the possibility of applying a wave finite element method (WFEM) to composite structure. The key feature of the WFEM is its capability of accurately analyzing the discontinuities in stress wavefront along with the discontinuities in velocities and strains. In addition, the numerical analysis of the WFEM is unconditionally stable and reduces numerical computation. This paper studies a periodically layered composite rod to analyze the dispersion and propagation of stress waves using the WFEM. The numerical results are compared with other numerical/analytical solutions, paying attention to the accuracy of computing the strong discontinuities in the stress wavefront as well as the dispersion of pulses in a heterogeneous elastic rod. It is shown that the WFEM can be used as an affordable tool for numerically solving wave propagation in composite structures.

Due to the incorporation of magnetic nanoparticles (MNPs), magnetically tuneable hydrogels have attracted considerable attention recently due to their ability to undergo remotely controlled large deformation. This work investigates the mechanics of the large deformation from the thermodynamics perspective for magneto-thermal sensitive hydrogels. The chemical thermodynamics of a temperature sensitive gel is first recapped before moving on to the thermodynamics of magnetism. Furthermore, an explicit energy form for the magneto-thermal sensitive hydrogel is adopted. The proposed field theory is implemented in a finite element method through the UHYPER subroutine. The finite element simulation results have been validated with analytical solutions at various temperatures and magnetic field strengths for MNPs entrapped PNIPAM hydrogel. We also utilize the numerical models to explain the interesting phenomena, including micro valves, bifurcation, and the opening of gel capsule for drug release delivery. The numerical deformation pattern for bifurcation is consistent with the experimental pattern, thus illustrating our theory and numerical method can provide future perspectives for device design of magneto-thermal sensitive hydrogel.

In this study, we numerically examine the effect of wing flexibility on the lift force generated by a modeled flapping wing that simulates an insect flight in hover mode. The flow field around the flapping wing is assumed to be two-dimensional (2D), and the flow equations are formulated with the notion of “immersed boundary” for easy handling of the moving-boundary problem. In the 2D framework, the wing chord is treated as an elastic filament. To account for the large deformation in the wing, the motion of the filament is modeled using a geometrically nonlinear equation for bending beams. Both sets of equations are then solved according to the fluid–structure interaction concept using appropriate numerical schemes. Time variation of lift force on the wing is calculated for different values of wing flexural rigidity. Effects of elastic deformation of the wing and interactions between the bending wing and vortical flow structure are discussed. Flexural rigidity that gives the highest average lift force on the wing is sought. This study affirms that the flexibility of wing and the vortex-pair capture phenomenon are crucial to the lift force generation in the flapping-wing mechanics.

A new functionally graded non-classical Timoshenko microbeam model is developed by using a variational formulation. The new model incorporates strain gradient, couple stress (rotation gradient) and velocity gradient effects and explains a power-law variation of two-phase materials through the thickness direction. The new model contains three additional material constants to account for the relative three gradient effects. The static bending, buckling and free vibration problems of the newly developed functionally graded material (FGM) beam are then analytically solved. Numerical results show that the differences between the prediction results of the current model and the classic model are significant when FGM beam thickness is very small, but they are diminishing as the thickness increases.

In this paper, the nonlinear damping and forced response behaviors of laminated composite cylindrical shells considering the internal damping of composite materials are investigated. Based on Donnell nonlinear shell theory, the dynamic governing equations of composite cylindrical shells with geometrical nonlinearity are established by using the Hamilton principle, in which the inherent material damping is taken into account by complex modulus method. The dependence of nonlinear damping on vibration amplitude and amplitude–frequency response are analytically obtained by the Galerkin method in conjunction with harmonic balance method. By comparing the results of natural frequency and modal damping with those in the literature, the correctness of the above theoretical analysis is verified. Furthermore, the effects of the circumferential wave number, lamination schemes, vibration amplitude and geometric configuration on the nonlinear damping and forced responses of the composite cylindrical shell with unidirectional, angle-ply and cross-ply laminations are analyzed. The results show that the damping dissipation capacity of the composite cylindrical shell is amplitude-dependent, and the effect of the amplitude on the nonlinear damping characteristics gradually decreases with the increase of the length-to-radius ratio. The ply angle not only affects the value of the resonance peak, but also significantly changes the degree of the soft and hard spring characteristics of the composite cylindrical shell. With the increase of internal material damping, the amplitude-frequency curve of the composite cylindrical shell changes from the coexistence of hard and soft characteristics to the only soft characteristics.

In this paper, a highly accurate analytical approximation solution method to a class of mixed-parity Duffing equation is proposed. The system may be attributed to the free vibration of laminated anisotropic plates or the simplified problem of particle vibration. The system is first analyzed qualitatively and subsequently, the analytic approximate periodic solution within the parametric range is constructed. The first approximate solution with a suitable initial condition can be obtained by using the proposed method. Subsequently, higher precision approximate solutions are constructed by combining Newton’s method and harmonic balance method. These analytical solutions have excellent approximation accuracy as verified by numerical solutions derived from exact analytical expressions.

In this study, the influence of material uncertainty on the vibration characteristics of the cracked functionally graded materials (FGM) plates is investigated. Extended stochastic finite element formulation is implemented to model the cracked FGM plate with material uncertainty using higher-order shear deformation theory (HSDT). The level set function is employed to track the crack in the FGM domain. The concept of partition of unity technique is implemented to enrich the primary variable with additional functions. The gradation of the material properties along the thickness direction is done using the power-law distribution. The first-order perturbation technique (FOPT) is incorporated in the methodology for stochastic vibration analysis. The convergence and validation study has been performed to verify the efficacy and accuracy of the formulation. Numerical results are obtained to show the effects of various influential parameters like crack length, gradient index, thickness ratio, and boundary condition on the covariance of the square of natural frequencies. The presented computational approach is accurate, efficient, and robust enough to investigate the vibration response of cracked FGM plates with material randomness.

As with any civil structure or mechanism, vehicular bridges can suffer structural damages which can conduct to devastating human and economic losses if they are not detected and corrected on time. In this work, a methodology based on the Shannon entropy index combined with statistical indexes and a fuzzy logic classifier to detect and locate a cable loss in cable-stayed bridges is proposed. Shannon entropy index is used to characterize the changes in the vibration signals associated with structural damage, which are integrated with statistical indexes for damage detection and damage location. On the other hand, the fuzzy logic classifier is used as a pattern recognition algorithm to detect structural damage automatically. For this study, the vibration data acquired experimentally from the Rio Papaloapan Bridge (Veracruz, Mexico) are analyzed. Results demonstrate the usefulness of the proposed method since 93.3% of effectiveness in the damage detection is obtained with a 100% of effectiveness in its location.