International Journal of Applied Mechanics

In this paper we study flow driven through a finite-length planar rigid channel by a fixed upstream flux, where a segment of one wall is replaced by a pre-stressed elastic beam subject to uniform external pressure. The steady and unsteady systems are solved using a finite element method. Previous studies have shown that the system can exhibit three steady states for some parameters (termed the upper, intermediate and lower steady branches, respectively). Of these, the upper and lower are stable to non-oscillatory perturbations, while the intermediate branch is always unstable. These upper and lower steady branches can (independently) become unstable to self-excited oscillations. We show that for some parameter combinations the system is unstable to both upper and lower branch oscillations simultaneously. However, we show that these two instabilities eventually merge together for large enough Reynolds numbers, exhibiting a nonlinear limit cycle which retains characteristics of both the upper and lower branches of oscillations. Furthermore, we show that increasing the beam pre-tension suppresses the region of multiple steady states but preserves the onset of oscillations. Conversely, increasing the beam thickness (a proxy for increasing bending stiffness) suppresses both multiple steady states and the onset of oscillations.

This paper analyzes the interaction of high Rayleigh number flow with conjugate heat transfer. The two-relaxation time lattice Boltzmann is used as a turbulent buoyancy-driven flow solver whereas the implicit finite difference technique is applied as a heat transfer solver. An in-house numerical code is developed and successfully validated on typical CFD problems. The impact of the Biot number, heat diffusivity ratio and the Rayleigh number on turbulent fluid flow and heat transfer patterns is studied. It is revealed that the thermally-conductive walls of finite thickness reduce the heat transfer rate. The temperature of the cooled wall slightly depends on the value of the buoyancy force. The heat diffusivity ratio has a significant effect on thermal and flow behavior. The Biot number significantly affects the mean Nusselt number at the right solid–fluid interface whereas the mean Nusselt number at the left interface is almost insensible to the Biot number variation.

This paper develops a family of optimized $n$-sub-step time integration methods for structural dynamics, in which the generalized trapezoidal rule is used in the first $(n-1)$ sub-steps, and the last sub-step employs $(n+1)$-point backward difference formula. The proposed methods can achieve second-order accuracy and unconditional stability, and their degree of numerical dissipation can range from zero to one. Also, the proposed methods can achieve the identical effective stiffness matrices for all sub-steps, reducing computational costs in the analysis of linear systems. Using the spectral analysis, optimized algorithmic parameters are presented, ensuring that the proposed methods can accurately calculate different types of dynamic problems such as wave propagation, stiff and nonlinear systems. Besides, with the increase in the number of sub-steps, the accuracy of the proposed methods can be enhanced without extra workload compared with single-step methods. Numerical experiments show that the proposed methods perform better in different dynamic systems.

Fluid flowing through reservoir pores not only generates poroelastic stress but also exerts seepage force on rock skeleton. However, the mechanism of seepage force is not clear. Traditional methods of analyzing wellbore stability and hydraulic fracture initiation are mainly focused on the poroelastic stress without the effects of seepage force. Based on the linear elasticity and consolidation theory, this paper analyzed the mechanism of seepage force and poroelastic stress, and presented an analytical solution for seepage force-induced stress around a vertical wellbore. It also introduced how to calculate poroelastic stress by exerting hypothetical body force and surface force. Through comparison and superposition of stress fields, this paper studied the change characteristics of the poroelastic and seepage force-induced stress under different borehole pressures and the effects of seepage force on the wellbore tensile failure. Numerical simulation results show that when fluid flows through the rock, using traditional models without considering, the effect of seepage force to calculate the borehole pressure-induced stress will result in lower calculation results. Compared with the traditional model, seepage force-induced circumferential tensile stress is larger, and the seepage force significantly reduces the formation breakdown pressure. Rocks near the borehole wall with lower permeability and larger Poisson’s ratio have a greater action of seepage force. When fluid flows through the reservoir, the effects of seepage forces cannot be ignored in the analysis of hydraulic fracturing and wellbore stability.

The available potential plant waste could be worthy material to strengthen polymers to make sustainable products and structural components. Therefore, modeling the natural fiber polymeric-based composites is currently required to reveal the mechanical performance of such polymeric green composites for various green products. This work numerically investigates the effect of various fiber types, fiber loading, and reinforcement conditions with different polymer matrices towards predicting the mechanical performance of such natural fiber composites. Cantilever beam and compression schemes were considered as two different mechanical loading conditions for structural applications of such composite materials. Finite element analysis was conducted to modeling the natural fiber composite materials. The interaction between the fibers and the matrices was considered as an interfacial friction force and was determined from experimental work by the pull out technique for each polymer and fiber type. Both polypropylene and polyethylene were considered as composite matrices. Olive and lemon leaf fibers were considered as reinforcements. Results have revealed that the deflection resistance of the natural fiber composites in cantilever beam was enhanced for several reinforcement conditions. The fiber reinforcement was capable of enhancing the mechanical performance of the polymers and was the best in case of 20 wt.% polypropylene/lemon composites due to better stress transfer within the composite. However, the 40 wt.% case was the worst in enhancing the mechanical performance in both cantilever beam and compression cases. The 30 wt.% of polyethylene/olive fiber was the best in reducing the deflection of the cantilever beam case. The prediction of mechanical performance of natural fiber composites via proper numerical analysis would enhance the process of selecting the appropriate polymer and fiber types. It can contribute finding the proper reinforcement conditions to enhance the mechanical performance of the natural fiber composites to expand their reliable implementations in more industrial applications.

This paper focuses on the buckling instabilities of periodic porous elastomers under combined multiaxial loading. A numerical model based on the periodic boundary condition (PBC) for the 2D representative volume element (RVE) is proposed, in which two proportional loading parameters are employed to control the complex stressing state applied to the RVE model. A homogenization-based orthogonal transformation matrix is established by satisfying the equality of the total work rate to realize a proportional multiaxial loading on the RVE. First, the transition behavior of buckling patterns of periodic porous structures is revealed through instability analysis for the RVE consisting of $2\times 2$ primitive cells with circular holes subjected to different proportional loading conditions. Simulation results show that the first-order buckling mode of RVE may change suddenly from a uniaxial shearing buckling pattern to a biaxial rotating buckling pattern at a critical loading proportion. Then the influences of the number of primitive cells in the enlarged RVE on the buckling behavior are discussed. When the number of primitive cells in any enlarging direction is odd, the points of buckling pattern transition of the enlarged RVEs vary significantly with the number of cells in RVE. When the number of primitive cells is even in both enlarging directions, there is no apparent difference for the critical buckling stresses of the enlarged RVEs.

This paper develops a new Hamiltonian nodal position finite element method for dynamic analysis of spatial flexible cable systems with large deformation. The dynamic governing equation is derived from finite elasticity theory. Logarithmic strain is applied to construct large deformation Hamiltonian canonical equations. An efficient second-order symplectic difference algorithm is built to solve the canonical equations numerically. A large strain conical pendulum system is analyzed numerically by the proposed method, and the numerical results are compared with those retracted from the existing Hamiltonian methods and Livermore Software Technology Corporation: dynamics (LS-DYNA). The proposed method is further verified by two tethered dynamic experiments involving large displacement motion and large deformation. The comparisons and verifications demonstrate that the proposed method is of symplectic conservation, has high accuracy and has stability for calculating flexible cable system dynamics with large deformation.

In this paper, a new plate structure has been found with the change of profile according to the sine function which we temporarily call as the sinusoidal plate. The classical plate theory and Galerkin’s technique have been utilized in estimating the nonlinear vibration behavior of the new non-rectangular plates reinforced by functionally graded (FG) graphene nanoplatelets (GNPs) resting on the Kerr foundation. The FG-GNP plates were assumed to have two horizontal variable edges according to the sine function. Four different configurations of the FG-GNP plates based on the number of cycles of sine function were analyzed. The material characteristics of the GNPs were evaluated in terms of two models called the Halpin–Tsai micromechanical model and the rule of mixtures. First, to verify this method, the natural frequencies of new non-rectangular plates made of metal were compared with those obtained by the Finite Element Method (FEM). Then, the numerical outcomes are validated by comparing with the previous papers for rectangular FGM/GNP plates — a special case of this structure. Furthermore, the impacts of the thermal environment, geometrical parameters, and the elastic foundation on the dynamical responses are scrutinized by the 2D/3D graphical results and coded in Wolfram-Mathematica. The results of this work proved that the introduced approach has the advantages of being fast, having high accuracy, and involving uncomplicated calculation.

In this work, an analytical method is presented to analyze the nonlinear static and dynamic buckling of imperfect stiffened double-layer functionally graded porous (FGP) shallow shells subjected to external pressure. The shallow spherical shell consists of two layers, where upper layer of shell is nonporous functionally graded (FG) material and the lower layer of shell is FG porous. This spherical shell is resting on elastic foundations, which consist of two-term Winkler–Pasternak’s model. Two FG porous distributions types consisting of symmetric porosity distribution (SPD) and nonsymmetric porosity distribution (NSPD) are investigated. The porous materials are assumed to vary through the thickness direction based on the assumption of a common mechanical feature of the open-cell foam. Utilizing the classical theory of shells considering geometrical nonlinearity based on von Kármán–Donnell relations and Hooke’s law, the governing equations of stiffened double-layer FG porous spherical shells are extracted. To discretize the partial differential equation of shell and obtaining the system equations of motion, the Galerkin method is applied. Regarding the discretized equation of motion, the explicit expressions for dynamic and static critical buckling load are determined. To investigate the dynamic behavior, the equation of motion is solved via a numerical method named Runge–Kutta approach, and then a presented approach by Budiansky–Roth is employed to obtain a critical load for the nonlinear dynamic buckling. The influence of various porosity distributions and coefficients of the shallow shell, elastic foundations, and geometrical characteristics on the nonlinear static and dynamic buckling analysis of imperfect stiffened double-layer FG porous shallow shells is examined.

According to the rise of technological interest in hydrogels, there is a growing necessity for precise mechanical and thermodynamic experimental characterizations. One of the common experimental protocols is applying combined extension-torsion loading on a cylinder. Therefore, we have proposed an analytical solution for the problem of torsion superimposed extension coupling with pH variation on a cylinder composed of the pH-sensitive hydrogel. Additionally, the Poynting effect as an inherently nonlinear phenomenon is studied for a hydrogel cylinder under extension-torsion loading. The finite deformation of a swollen cylinder is investigated using a constitutive model that captures network stretching, mixing of polymeric network and solvent, mixing of mobile ions with the solvent, and acidic groups’ dissociation. To evaluate the analytical solution accuracy, 3D finite element analysis (FEA) has been carried out for the same problem. In this regard, it is required to develop a user-defined subroutine, UHYPER, for pH-sensitive hydrogels; the developed subroutine is validated via free-swelling and constrained swelling problems. Compared to the FEA, the presented analytical solution is more interesting regarding its low computational cost. It is perceived that the computational cost of the analytic solution is much lower than the one required for FE analysis (around 1%). Thus, the proposed solution can be utilized as aneffective toolto examine each factor on the swelling behavior of hydrogels, including mechanical properties as well as loading parameters. Moreover, the developed analytical solution can be employed for calibrating material parameters. Finally, Poynting effects are examined for various axial stretches and twists, pH values, and cross-linked densities.

Numerous structure geometries are available for cellular structures, and selecting the suitable structure that reflects the intended characteristics is cumbersome. While testing many specimens for determining the mechanical properties of these materials could be time-consuming and expensive, finite element analysis (FEA) is considered an efficient alternative. In this study, we present a method to find the suitable geometry for the intended mechanical characteristics by implementing machine learning (ML) algorithms on FEA results of cellular structures. Different cellular structures of a given material are analyzed by FEA, and the results are validated with their corresponding analytical equations. The validated results are employed to create a data set used in the ML algorithms. Finally, by comparing the results with the correct answers, the most accurate algorithm is identified for the intended application. In our case study, the cellular structures are three widely used cellular structures as bone implants: Cube, Kelvin, and Rhombic dodecahedron, made of Ti–6Al–4V. The ML algorithms are simple Bayesian classification, K-nearest neighbor, XGBoost, random forest, and artificial neural network. By comparing the results of these algorithms, the best-performing algorithm is identified.

Fiber-reinforced polymer composites exhibit orthotropic mechanical properties and particularly low strength in the out-of-plane direction. The use of classical failure criteria that consider transverse isotropy to evaluate these composite materials implies an overestimation of their out-of-plane strength, which could lead to a nonconservative and even catastrophic design. The Molker failure criteria developed for orthotropic materials consider the LaRC05 failure modes as a basis, with two additional failure modes for the out-of-plane direction of noncrimp fiber (NCF)-reinforced composites. Given the similarity in configuration and orthotropic behavior of unidirectional fiber fabric reinforced composites to NCF-reinforced composites, Molker failure criteria are implemented and applied in this research to determine the initiation of out-of-plane failure in unidirectional fiberglass fabric composites. The criteria are programmed in the form of a module coupled to a constitutive model available in a finite element method (FEM) package. Then, the mechanical properties and failure parameters of the unidirectional fiber-reinforced composite are determined. Model validation is accomplished by comparing numerical and experimental results of out-of-plane failure in a corrugated panel. In addition, several failure criteria used in unidirectional fiber-reinforced composite that consider transverse isotropy are evaluated. The results of critical load at the onset of transverse out-of-plane failure obtained by using the Molkerorthotropic criterion prove to be superior in accuracy compared to those obtained with the criteria commonly applied to this type of materials.