Forces in mechanics最新文献

The dual thickness dished shells are made of conical frustum with a closed stiff top at the smaller diameter end of the frustum. The dished shells are categorized as dual-thickness because of higher thickness of the top circular region than that of the conical region. The higher thickness of top flat circular portion makes this more stiffer. The buckling behaviour of these shells is similar to that of arches, spherical caps and shallow conical frustums. The variation in curvature of these shells and different stiffnesses of the conical and top circular region makes them very interesting and innovative. Making the top circular region stiffer avoids the need for stiff support in the top circular region for practical applications under uniform pressure. In the present study, a nonlinear finite element analysis on metallic dished shells of dual-thickness is attempted by varying different geometrical parameters such as thickness of conical region, height and top flat region radius of the shell under uniform pressure. This parametric analysis is carried out to find out the effect of elastic and elastic-perfectly-plastic material properties, boundary conditions and imperfection sensitivity of Eigen-mode type axisymmetric imperfections on the critical buckling pressure. It is found that material plasticity has a significant effect on the critical buckling pressure of dual-thickness dished shells. The effect of the axisymmetric Eigen-mode imperfections on critical buckling pressure is significant for the elastic material model and very small with elastic-perfectly-plastic material models. The information collected from the current study can be used for the detailed design of dual thickness dished shells.

The present study considers the nonlinear vibration behavior of a beam with general boundary conditions that carry an electrical current in the magnetic field. This paper discusses the magnetic couple, the transverse magnetic force, the electrical current, and the damper. By contrast, the magnetic field is selected as an arbitrary function of time. Under certain hypotheses, Hamilton's principle is used along with Maxwell's equations to derive the governing equation. An elastically restrained beam carrying an electrical current is also solved using Galerkin's method under a magnetic field. Thus, the effect of the rotational and the translational support flexibilities, the magnetic field, and other parameters are evaluated. For a more detailed investigation, some numerical examples are investigated to present the simplicity and efficiency of this formulation. Based on the numerical results, it is clear that the natural frequency of the ferromagnetic beam is sensitive to the angle and magnetic field. By increasing magnetic field intensity, the magnitude of the natural frequency of the beam increases. But with the increase of the angle, the frequency value decreases. Therefore, at larger angles, the impact of the intensity of the magnetic field will be less. Also, it is determined from the results that the beam deflection in various magnetic fields indicates a significant effect of the boundary conditions, not only on the dynamic response of a damped beam but also on the rate of damping of the response. The dynamic response under the magnetic field is decreased when the beam experiences a stiffer constant in its support. The results are shown that the effect of stiffening for the transitional support is more significant than that of the rotational support. Also, the influence of the boundary constraints becomes smaller when the magnetic field becomes smaller.

In this investigation, we study experimentally the evolution of both the deformation and the stress during the necking process of a thin metal sheet subject to uniaxial tension. The deformation over the sample surface is obtained using the optical technique of Digital Image Correlation (DIC), which maps out full-field displacement over a two-dimensional (2D) domain. The stress field associated with the measured deformation is determined using the technique developed by Liu [18], where if the deforming material remains isotropic, the stresses can be computed based on the measured deformation by solving the equation of equilibrium together with appropriate traction boundary conditions. The deformation measurement indicates that after the initiation of the neck the deformation in areas outside the neck is frozen, confirming what Bridgman [2] has speculated, and the deformation within the neck area continues to increase till final failure. There is never a reversal in deformation and, as a result, all material particles in the necking zone only experience softening but not unloading. The results also reveal some unique and interesting patterns of the stress field over the necking zone. Their implications on the analysis and modeling of the necking process are discussed.

In real-world physics phenomena, the boundary conditions of structural members in the structural beam systems affect the system response. Also, moving load or mass problems are used widely in many engineering fields, such as structural, transportation, mechanical engineering, etc. Therefore, it is necessary to study the effect of boundary conditions on beam vibrations. Hence, a semi-analytical approach for the Timoshenko beam with various boundary conditions under moving mass is presented in this paper. Dynamic Green Function is introduced for modeling the beam under moving mass. An accurate formulation is illustrated for modeling a Timoshenko beam under moving mass with different boundary conditions. Finally, some examples demonstrate to assess of the effect of different boundary conditions, the mass ratio of moving mass, and the speed of moving mass. The numerical results are shown the efficiency and simplicity of the present approach. Based on the results, it is found that the mass ratio affects the dynamic response shape. For moving mass, the delay of the maximum dynamic deflection with respect to the mass position, increases with the speed at the higher speeds. But for smaller values of the speed, the same results of the maximum dynamic deflection for the moving load model along with the moving mass model are obtained. On the other hand, the maximum dynamic deflection points of the curves move slightly towards the right end of the beam with an increasing mass ratio. Also, the location of the constraint in the asymmetric beams is more significant in dynamic response. It is found that the dynamic behavior of the beam under moving mass changes dramatically based on the type of boundary conditions. Furthermore, the displacement obtained for each boundary condition decreases with increasing mass speed.

This work presents an analytical asymptotically-correct micromechanics model that helps to predict the effective material properties of a unidirectional composite material. The conventional and numerical approaches estimate the homogenized material properties of composites for their defined component volume fractions, their constituent properties and configurational geometry. Presently these approaches are based on kinematic assumptions such as having displacement or stress components vary through the cross section for beam like structures or through the thickness for plate like structures according to certain predefined functions that doesn’t always logically follow the 3D analysis. In the present formulation, the micromechanics model is developed by accommodating all possible deformations without assuming the displacement function or stress components. These are derived by minimizing the potential energy in terms of generalized strain measures. In the present formulation, Berdichevsky’s Variational Asymptotic Method (VAM) is employed as a mathematical tool to accomplish the homogenization procedure. The Hashin-Rosen model popularly referred to as the Concentric Cylinder Model (CCM) serves as the framework to estimate all the relevant homogenized elastic moduli and coupling coefficients. The derived quantities of interest are obtained as closed form expressions which are functions of the properties of the reinforcement material, the matrix material, their volumes fraction and the geometry of their relative arrangement. These expressions are arrived following the 3D elasticity governing rules by satisfying the interfacial displacement continuity and transverse stress equilibria conditions at the reinforcement and matrix materials interface. The developed expressions for the elastic moduli, shear moduli and Poisson’s ratios of few typical polymer and metal matrix composite materials are validated with some of the relevant results available in the literature.

Studying electrokinetic swirling flows of ionic tribological fluid in a squeezing/splitting scenario has drawn a lot of interest due to its extensive dispensations in mechanical and manufacturing engineering. The present modelling and simulation-based study deals with an in-depth physical exploration of electric double layer (EDL) aspects in a swirling flow via a squeezing/splitting perforated channel filled with ionic tribological fluid when subjected to a high-power magnetic field with Hall current. The rudimentary momentum equations are presented by assigning partial differential equations (PDEs), which are then transmuted into non-linear ordinary differential equations (ODEs) using a compatible similarity substitution. The reduced system of coupled non-linear ODEs with proposed boundary data is dealt with numerically by dint of Runge-Kutta-Fehlberg (RKF45) formula-based shooting scheme, namely Mathematica in-built routine function bvp4c. By plotting distinctive graphs and tables, the physical impacts of emerging model parameters upon the moment profiles and engineering entities of interest are explored and interpreted. Simulated outcomes unravel with an intensification in electroosmosis and rotation parameters, the fluid pressure is discerned to rise near the channel plates while a contrary affinity prevails in the central passage. The shear impedance can be minified by adjusting the squeezing velocity. The imprinted flowlines plots unfold that the reverse flow is noticeable with the negative suction parameter. Our squeezing flow model might apply to tunnelling, semiconductors, sensing and control systems, spacecraft designing, etc.

When modeling composite materials at small scales, the consideration of nonlocal effects is fundamental. In addition, the overall response of matrix-inclusion composites is strongly affected by the behavior of the interface between inclusion and matrix. This can be attributed to a possible detachment of the constituents as well as the high interface-to-volume ratio especially for nano-sized inclusions. Peridynamics is a nonlocal theory that is suitable to introduce a length-scale into a continuum description and take into account nonlocal interactions. Complex interface models within a peridynamic framework are, however, rarely studied. The objective of this work is to present a modeling approach to nonlocal interfaces accounting for opening and degradation within the framework of continuum-kinematics-inspired peridynamics (CPD). The proposed method is employed to study nonlocal effects in matrix-inclusion composites with focus on the effect of nonlocal interfaces. In our approach, the nonlocal interface is modeled as a finite thickness interface, i.e. a region where the subdomains overlap. Within this region, the constituents are pair-wise connected through interface bonding forces that follow a characteristic force-opening law. In computational experiments, our model captures the influence of the strength and size of the interface as well as the inclusion volume fraction on the overall response. In particular, nonlocality manifests itself through a “smaller–stiffer” material behavior and an increased influence of the interface, which highlights the importance of an appropriate nonlocal interface model.

We study a version of the two-degree-of-freedom double pendulum in which the two point masses are replaced by rigid bodies of irregular shape and nonconservative forces are permitted. We derive the equations of motion by analysing the forces involved in the framework of screw theory. This distinguishes the work from similar studies in the literature, which typically consider a double pendulum composed with rods and assume equations of motion without derivation. The equations of motion are solved numerically using the fourth-order Runge-Kutta method to show that decreasing the friction of the axles can cause the trajectory of one of the pendulums to become aperiodic. The stability of steady state solutions is also analysed.

Primary total hip replacement surgery has an undisputable reputation as a widely successful orthopaedic operation, but it is beset by a phenomenon known as stress shielding. The cause of stress shielding is multifaceted. However, its reduction is reported to be hinged on the optimal design of prosthetic implants. Yet, to date, the design of a hip implant profile that behaves biomechanically similar to the natural physiological load-bearing zones of the femur remains an open problem. Along this vein, this paper instantiates an inquiry into the development of a framework that couples the capability of the finite element analysis (FEA) with that of machine learning methods toward the discovery of optimal design parameters for a customized hip implant. First, premised on the properties of a commercial normal-stem hip implant, a baseline computer-aided design (CAD) parametric model was created. From the baseline CAD model, a database of 120 hip implant profiles is established from the perturbation of the lateral edge, lateral angle, and the ratio of the radial cross-sectional areas of the implant. Next, the validation of the developed finite element procedure was conducted on a healthy intact femur and detailed numerical simulations were undertaken to assess the stress shielding (SS) attributes of all hip implants in the established database. The ensuing stress and strain data from the FEA is then deployed to ward a data-driven inverse model based on the random forests machine learning algorithm. Results-wise, the validation of the static analysis on the intact femur yielded von Mises stresses that matched those reported in published studies. Moreover, other results from the FEA revealed that a rectangular cross-sectioned hip implant resulted in the highest SS in the four zones of the proximal femoral compared to the trapezoidal cross-sectioned implant. Further, the inverse RF model exhibited excellent predictive capability and was subsequently employed towards the retrieval of the optimal geometric parameters that will manifest minimal stress shielding effect.

The phase field approach has proved to be efficient and has received ample attention amongst the available techniques to model fracture. However, high computational cost still imposes substantial difficulties in the phase-field simulation of fractures. This contribution is based on a recently proposed variational approach for spatial adaptivity in a phase-field model of fracture. The main idea is to consider the regularisation length $ϵ$ as a space-dependent variable in the argument of the energy functional. We extend this now by implementing a strain energy split to ensure that only the tensile energy drives the crack propagation. The displacement, phase field, and optimal regularisation length are then determined locally by minimisation of the modified energy functional. Subsequently, the computed optimal regularisation length is used to refine the mesh size locally. The resultant solution procedure is implemented in the finite element library FEniCS. Numerical investigations on selected examples of different fracture modes demonstrate that the spatially adaptive phase field model has a comparable convergence rate, but a subjacent energy convergence curve resulting in significant computational savings. Moreover, it also computes the peak force more accurately illustrating its potential for usage in practical applications.