End Conditions Research Articles

Buckling and free vibration analysis of bio-inspired laminated sandwich plates with helicoidal/Bouligand face sheets containing softcore

Helicoidal laminates inspired by mantis shrimp crustacean can sustain higher loads compared to conventional laminated structures. However, there is still a lack of bending studies on the plates inspired by these helicoidal structures. The buckling and free vibration studies have been undertaken in the present work on the laminated composite and sandwich plates inspired by the helicoidal structures of the biological characters. Investigations are carried out using higher-order zigzag theory. For sandwich plates, the top and bottom face sheets are assumed to be made up of helicoidal layup schemes. Different kinds of helicoidal schemes, namely, recursive, exponential, semicircular, Fibonacci, and linear helicoidal are considered during the analysis. The buckling and free vibration behavior of helicoidal-based laminated sandwich plates are compared with the conventional laminated sandwich plates such as uniform distribution and cross-ply configurations. The influence of the number of layers, helicoidal schemes, geometric properties, and end conditions on the buckling and free vibration analysis of bio-inspired helicoidal laminated composite and sandwich plates is carried out in detail.

On energy absorption and low-velocity impact response of functionally graded graphene oxide powders-reinforced nanocomposite panel on the viscoelastic substrate

Curved panels are used for ships due to complex situations that can be under external loading. So, it is very important to know about the stability related to the curved system under Low-Velocity Impact (LVI). To improve the stability of this kind of structure, graphene oxide powders (GOPs) are added to its matrix. In addition, the contact force between the impactor and shell is evaluated by implementing Hertz contact theory. So, in the current work, as a first attempt, energy absorption and low-velocity impact response of functionally graded graphene oxide powders-reinforced nanocomposite panel on the viscoelastic substrate is presented. Higher-order shear deformation theory (HSDT), which has twelve factors, is employed to determine the displacement domains. Also, the minimum potential energy technique is designated to obtain the governing equations and end conditions. Moreover, Galerkin and Newmark methods are chosen to solve the relationships. The governing equations related to the curved system under external excitation aimed at achieving the LVI and dynamic outputs are determined by the connection of Galerkin and Newmark methods. The uniqueness of this research is considering the impacts associated with HSDT and various Boundary Conditions (BCs) in addition to considering FG oxide powder reinforcement. The outputs segment displays the effects related to the BCs, the radius of the impactor, mass, and velocity, as well as the weight fraction related to the GOPs on contact force, the indentation, and the indenter velocity.

Autonomous optimization of cutting conditions in end milling operation based on deep reinforcement learning (Offline training in simulation environment for feed rate optimization)

Autonomous optimization of cutting conditions in end milling operation based on deep reinforcement learning (Offline training in simulation environment for feed rate optimization)

Nonlinear Thermal-Magneto-Mechanical Vibration Analysis of Single-Walled Embedded Branched Carbon Nanotubes Conveying Nanofluid

Abstract In this present study, the nonlinear thermal-magneto-mechanical stability and vibration of branched nanotube conveying nano-magnetic fluid embedded in linear and nonlinear elastic foundations are analyzed. The governing equations are established via Euler–Bernoulli theory, Hamilton’s principle, and the nonlocal theory of elasticity. The fluid flow and thermal behaviors of the nanofluid are described using modified Navier–Stokes and conservation of energy equations. With the aid of the Galerkin decomposition technique and differential transformation method (DTM), the coupled thermos-fluidic-vibration equation is solved analytically. The analytical solutions as presented in this study match with an existing experimental result and as such used to explore the influences of nonlocal parameters, downstream or branch angle, temperature, magnetic effect, fluid velocity, foundation parameters, and end conditions on vibrations of the nanotube. The results indicate that decreasing temperature change and augmenting the nanotube branch angle decreases the stability for the prebifurcation domain but increases for the post-bifurcation region. Furthermore, the magnetic term possesses a damping or an attenuating impact on the nanotube vibration response at any mode and for any boundary condition considered. It is anticipated that the outcome of this present study will find applications in the strategic optimization of designed nano-devices under thermo-mechanical flow-induced vibration.

Pre-Stress Linear and Nonlinear Buckling of Cold-Formed Steel Built-up Box Studs

In construction industry, cold-formed steel sections become more pertinent in place of hot-rolled steel members. The design guides for CFS are inadequate and hence it is substantial to investigate their governing behaviours as material failure and structural instability (buckling). This study aims to analyse how the buckling behaviours of face-to-face built-up box short columns are administrated by the application of end plates with three different welded spacing. Sixgeometric models were analysed with ANSYS 2020 R1, numerical software, to evaluate the pre-stress linear and non-linear buckling loads of built-up box studs. The results distinguish the application of end plates and the most effective welded spacing for built-up geometry. It is significant that end plates are more advantageous to resist the maximum compressive loads whereas 509.6 mm is the relevant welded spacing for built-up box section. It is additionally suggested to analyse the governing of weld spacing and end conditions of various built-up geometries: box, sigma and I studs through numerical and experimental analysis.

An improved density peaks clustering algorithm based on natural neighbor with a merging strategy

Density peaks clustering (DPC) is a novel density-based clustering algorithm that identifies center points quickly through a decision graph and assigns corresponding labels to remaining non-center points. Although DPC can identify clusters with any shape, its clustering performance is still restricted by some aspects. Firstly, DPC works poorly on manifold datasets with different densities. Secondly, DPC is sensitive to the cutoff parameter dc. For the sake of addressing these issues and improving the performance of DPC, an improved density peaks clustering algorithm based on natural neighbor with a merging strategy (IDPC-NNMS) is proposed. IDPC-NNMS identifies a natural neighbor set of each data to obtain its local density adaptively, which can effectively eliminate the impact of the cutoff parameter on final results. Then, sub-clusters are formed after selecting as many center points as possible and allocating labels to remaining non-center points. These sub-clusters are merged by a novel merging strategy until the end conditions are satisfied. The performance of IDPC-NNMS is evaluated on both synthetic and real-world datasets, which fully proves the effectiveness and superiority of the proposed IDPC-NNMS algorithm.

Aeroelastic flutter behaviour of beam: effect of graded GPL and porosity

The present study investigates the aeroelastic flutter characteristics of the graphene platelets (GPL) reinforced metal foam beam. Closed-cell metal foam beams having graded distribution of pores and functionally graded reinforcement of GPLs are considered in this study. The closed-cell metal foam model has been used for deriving the mechanical properties of the foam matrix, which makes provision for determining the relation between the co-efficient of porosity and the co-efficient of density. Modified Halpin-Tsai micromechanics is used to obtain the effective Young’s modulus of the GPLs reinforced composite beam, Density and Poisson’s ratio are calculated with the help of the rule of mixture. The Hamilton’s principle together with the Ritz method, employing the first-order piston theory gives the governing equations of motion for aeroelastic flutter characteristics of the beam for different end conditions. Juxtaposition of dimensionless natural frequencies with the results previously published by others is executed for validating the correctness of the approach followed in the present model. A study of various parameters has been executed, and the results in tables and graphs present the influence of porosity as well as GPLs reinforcement, different boundary conditions and thermal loading on aeroelastic flutter characteristics of the FG-GPL reinforced metal foam beam.

Sress-strain analysis and optimization of the geometric shape of cylindrical oilfield reservoirs

The paper sets forth an approach for calculating and optimizing the geometric shape, taking into account the physical nonlinearities of the material of oilfield reservoirs and the end conditions of supports. An effective calculation technique based on finite difference methods has been developed. On the basis of the developed methods, a computational algorithm was created, a set of applied programs was compiled. An analysis of the calculation results based on the developed computational technique showed that the solution of the problems of determining the stress-strain behavior of shells must be carried out taking into account the physical nonlinearity. The influence of various factors on the stress-strain behavior of the reservoir was found out. A general method for the linearization of a thin structure with changeable geometric parameters is proposed, which has accelerated convergence. Based on the results of the calculations, concrete formulas and diagrams have been compiled that can be used in engineering practice. Keywords: shell; cylindrical oilfield reservoir; nonlinear model; finite difference method.

Cubic spline interpolation with optimal end conditions

Traditional end conditions for cubic spline interpolation consist of values, the first or the second derivatives of interpolated functions on the boundary interpolation knots. The not-a-knot end condition proposed by de Boor (1985) is a kind of end condition of cubic spline interpolation for the practical application without the requirements of the derivatives at the end knots. However, a significant disadvantage of such end condition is that there is a sharp decrease in the accuracy of the interpolation at boundary intervals. In this paper, by changing the locations of two spline knots in not-a-knot end condition, we propose the optimal arrangement of shifted spline knots for cubic spline interpolation. The proposed scheme leads to an approximately 3.4 times increasing in the accuracy of the interpolation compared to the de Boor’s not-a-knot end condition. Furthermore, we also present the optimal end conditions of cubic spline interpolation to approximate the first and the second derivatives of interpolated functions. The representative examples show the effectiveness and the superiority of the proposed method.

Lattice Boltzmann simulation of thermo-magnetic natural convection in an enclosure partially filled with a porous medium

A theoretical analysis of incompressible magnetohydrodynamic (MHD) non-Darcian hydrogravitational convection in a square enclosure partially filled with a highly permeable medium in presence of transverse magnetic field is presented. A non-Darcy model is utilized for the porous region featuring both Darcian linear drag and second order Forchheimer drag components with Brinkman no-slip at the walls. The horizontal (i.e., bottom and Top) wall boundaries are considered adiabatic and impermeable, while the side walls (hot and cold walls) are maintained with different thermal values. The governing momenta and thermal conservation equations with appropriate end conditions are solved by Lattice Boltzmann method (LBM). A parametric examination of the impact of Hartmann number (0 < Ha < 50), Darcy number (0.0001 < Da < 0.1), and Rayleigh number (103 < Ra < 106) on temperature contours and streamline patterns for Helium gas (Prandtl number (Pr) = 0.71) is conducted. The heat flux distributions on the side walls and centre-line velocity are also computed. With greater Darcy number and Rayleigh number, Nusselt number is boosted at the left hot wall and the right cold wall. However, Nusselt number increases as one descends the hot wall toward the lower adiabatic boundary, and subsequently increases asone ascends the cold wall toward the upper adiabatic boundary.

On Effects of Shear Deformation on the Static Pull-in Instability Behaviour of Narrow Rectangular Timoshenko Microbeams

MEMS devices utilize electrostatics as preferred actuation method. The accurate determination of pull-in instability parameters (i.e., pull-in voltage and pull-in displacement) of such devices is critical for their correct design. It should be noted that similar to parallel plate capacitors, the electrostatic force between the surface of the deformable microbeam and stationary ground is non-linear in nature. Hence the analysis associated with MEMS devices is always inherently non-linear. In the literature, these devices have been majorly analyzed as Bernoulli-Euler microbeams with cantilever or clamped-clamped beam end conditions. However, Dileesh et al. (doi: 10.1115/ESDA2012-82536) have studied the static and dynamic pull-in instability behavior of slender cantilever microbeams by developing a six-nodded spectral finite element based on the Timoshenko beam theory (TBT-SFE). They have demonstrated the accuracy of the TBT-SFE by comparing their results with corresponding results of COMSOL-based three-dimensional finite element simulations. In addition, effects of shear deformation also start to play significant role as the beam thickness-to-length ratio increases. In this paper, authors have developed the TBT-SFE based on the work by Dileesh et al. for the case of statics. However, unlike Dileesh et al. where they have developed a six-nodded TBT-SFE, authors have investigated the best combination of number of nodes per element and total number of elements to carry out the study. For this purpose, authors have first calculated results of the maximum beam transverse displacement, for a shear deformable propped-cantilever microbeam under the action of uniformly distributed transverse load, obtained by utilizing the developed TBT-SFE with different combinations of number of nodes per element and total number of elements. These results are then compared with corresponding analytical results available in the literature to arrive at the best combination of number of nodes per element and total number of elements for the electrostatic-elastic analysis. In the second step, the finalized TBT-SFE is utilized to determine static pull-in instability parameters of narrow microbeams with various fixity conditions and beam thickness-to-length ratios. This study highlights the importance of transverse shear effects on pull-in instability parameters of Timoshenko microbeams.

Finite element model for advanced analysis of plane steel frames with hinged end conditions including von Mises criterion

Traditionally, the design of steel structures is carried out in two steps: first, the structural analysis is performed, and then the cross-sections and structural members are checked individually. In contrast, in the advanced analysis, the effects related to global (P-Δ) and local (P-δ) instabilities and to the degradation of material stiffness are incorporated; therefore, there is no need to verify the resistance capacity of the structural members separately, which allows a better use of the load capacity of the structural system. Generally, research developed in this area of study is based on the classical Euler-Bernoulli theory; however, in the case of short elements, an analysis that includes the shear effects and the interaction between normal and shear stresses on cross-section yielding becomes necessary. Thus, this work aims to study the behavior of plane steel frames considering the influence of shear deformations by using advanced analysis. A geometrically exact formulation for analysis of rigid-hinged and hinged-rigid elements is presented. The proposed numerical methodology is implemented in finite element software and takes into account Timoshenko’s kinematic hypothesis, the distributed plasticity approach, residual stresses, and second-order effects. To assess the plastification state of the structural elements, the von Mises yield criterion is applied. From numerical examples available in the literature, the efficiency of the software in predicting the nonlinear behavior of steel frames is assessed. It is concluded that for short beams, the adoption of the von Mises criterion during the analysis leads to lower load capacities, compared to the results obtained considering only the normal stresses in the evaluation of the plastification state of the cross-sections.

On buckling of layered composite heavy columns—Effect of interlayer bonding imperfection

Buckling loads of partial composite columns under distributed axial loads is investigated in this paper for the first time. The interlayer interaction corresponding to the level of interfacial bonding imperfection in the layered heavy composite columns is formulated in the model by a shear slip/stiffness modulus. Governing differential equations and boundary equations are derived and represented in a general dimensionless form. A semi-analytical solution is applied to the governing buckling equations of the presented model using power-series technique to extract critical loads of partial composite columns. Five different classical end types are considered namely clamped–clamped (C-C), clamped-pinned (C-P), clamped-sliding (C-S), clamped-free (C-F) and pinned–pinned (P-P). Also, for two extreme cases of non-composite/zero-interaction and full-composite/perfectly-bonded layered columns, exact closed-form characteristic buckling equations are introduced. A convergence study is conducted to ensure stability of the applied power-series solution. It is demonstrated that the obtained buckling loads for partial composite columns with different end conditions approach those obtained from the exact closed-from solution for the full-composite extreme case when the interfacial shear modulus approaches infinity. Effect of imperfect bonding between the column layers and slip on critical buckling loads is investigated. It is shown that a more realistic model based on the partial composite interaction hypothesis predicts critical loads that are less than those based on idealized composite columns with perfect interfacial bonding.

Coupled Newmark beta technique and GDQ method for energy harvesting and vibration control of the piezoelectric MEMS/NEMS subjected to a blast load

The controlled vibration and energy harvesting from a sandwich nanobeam, including two piezoelectric layers and a nanocomposite core, is investigated with the aid of nonlocal strain gradient theory. The nanobeam system is placed on an elastic substrate and under shockwave. The core layer is made of a reinforced composite made of a matrix polymer and carbon nanotubes (CNTs) along with carbon fibers (CF). The formulations along with end conditions are attained via Hamilton's principle and solved by the generalized differential quadrature method (GDQM) coupled with the Newmark beta method. Additionally, the vibration is controlled with two differential and integral gains. The impact of parameters such as elastic foundation, control gains, nonlocal factors, and parameters affecting the core material on forced vibration as well as energy harvesting is explored in detail. The current results are validated utilizing other publications. This work can be a basis for future studies on energy harvesting and controlled vibration on small scales.

Optimization of Advanced Laboratory Monotonic and Cyclic Triaxial Testing on Fine Sands

Abstract Monotonic and cyclic triaxial testing provides key information for a wide range of sensitive geotechnical problems. This paper assesses the potential impact on stress-strain measurements of several error sources and discusses how test quality may be improved. External volume gauges are shown to be subject to significant errors that depend on the pressure level. While high-resolution local radial strain measurement presents considerable challenges, especially in long-duration cyclic tests, problems with “floating” radial-belt and alternative “L-configuration” systems were overcome by steps that allow strains as low as 10−4 % to be resolved reliably. Sample end conditions are shown more important than is commonly appreciated. Employing smooth, enlarged, and lubricated end platens can avoid the recording of misleadingly high shear resistances, which are most significant with relatively loose specimens tested under low effective stresses. Stiffnesses and dilation trends were also recorded more reliably in tests employing smooth, enlarged, and lubricated end platens. The arrangements overcome significant strain errors even in tests employing local instruments and specimens with initial height-to-diameter ratios of 2.

Nonlinear dynamics of traveling beam with longitudinally varying axial tension and variable velocity under parametric and internal resonances

In this investigation, the nonlinear dynamics of an axially accelerating viscoelastic beam on a pully mounting system have been analyzed. The axial tension of the beam is modeled as a function of the traveling velocity, support stiffness parameter as well as spatial coordinate. Geometric cubic nonlinearity in the equation of motion is due to elongation in the neutral axis of the beam. The integro-partial differential equation of motion of the axially accelerating beam associated with the simply supported end conditions is solved analytically by adopting the direct perturbation method of multiple time scales. As a result, a set of complex variable modulation equations is generated, which governs the modulation of amplitude and phase. This set of modulated equations is numerically solved to explore the influence of the support stiffness parameter upon the stability and bifurcation of the beam which has not been addressed in the existing literature. Apart from this, the impact of fluctuating velocity component, viscoelastic coefficient, longitudinal stiffness parameter, internal and parametric frequency detuning parameters on the stability and bifurcation analysis is studied, revealing significant dynamic characteristics of the traveling system. The fourth-order Runge–Kutta method is applied is to find the dynamic solution of the system. The system displays stable periodic, quasi-periodic, and mixed-mode dynamic responses along with the unstable chaotic behavior for a specific set of system parameters. The results obtained through an analytical–numerical approach may help the design and operation of an axially moving beam.

Nonlinear flutter of 2D variable stiffness curvilinear fibers composite laminates by a higher-order shear flexible beam theory with Poisson’s effect

In this work, the nonlinear supersonic panel flutter characteristics of two-dimensional variable stiffness curvilinear fibres based laminated composite panels are studied using a higher-order shear flexible theory represented by sine function coupled with first-order approximation leading to quasi-aerodynamic theory. The structural formation takes care of geometric nonlinearity with von Karman’s assumptions. The beam constitutive equation is modified for the laminated beam with general lay-up by accounting for Poisson’s effect. The nonlinear dynamic equilibrium equations developed by Lagrangian equations of motion are solved using finite element approach in conjunction with the direct iterative solution procedure. For limit cycle oscillation, critical dynamic pressure is predicted iteratively through eigenvalue analysis, thereby identifying the first coalescence of vibrational modes. Also, the flutter behavior of two-dimensional panel under static differential pressure is investigated considering nonlinear static equilibrium position of panel obtained by Newton-Raphson’s iterative approach and then followed by modes coalescence approach. These solution procedures are tested against the results in literature. A thorough numerical investigation is done to show the effect of the curvilinear fiber path orientation, limited cycle amplitude, static differential pressure, panel thickness, panel end condition flexibilities and thermal environment on the nonlinear supersonic panel flutter of two-dimensional variable stiffness laminated panels.

Vibration–impact study on the functionally graded graphene nanoplatelets reinforced composite curved open-type shell

This paper investigates the stability of the curved system reinforced by graphene nanoplatelets (GPLs) under low-velocity impact. Hertz contact theory is employed in order to model the contact force between the shell and the impactor. In order to acquire the displacement domains, higher-order shear deformation theory (HSDT) with twelve parameters is used. The governing equations, in addition to end conditions, are attained by the Minimum potential energy method. Then the formulations are solved through the Galerkin method as well as the Newmark method. By coupling Galerkin and Newmark methods, we solved the governing equations of the curved system under external excitation for attaining the dynamic and low-velocity impact responses. The results section shows the influence of boundary conditions, velocity, mass, and radius of the impactor, and the weight fraction of GPLs on indenter velocity, contact force, and the indentation of the GPLs reinforced open-type shell under low-velocity impact.

Investigation of flexural and shear failure modes of tapered castellated steel beams using expansion plates

Using modern technologies for fabricating steel, I-beams can be easily made by welding, and hot-rolled beams can often be produced at an economical price with slender webs and equal flanges. Experimental and theoretical studies of the behavior of tapered castellated steel beams were carried out. Due to the cost reductions associated with tapered castellated steel beams, they are a feasible alternative to prismatic components. This study assessed the influence of tapered castellation on the bending capacity and flexural stiffness of tapered castellated steel beams (TCBs) with simply supported end conditions experimentally and theoretically. Four three-point bending tests on TCBs with H/h values of 1, 1.2, 1.4 and 1.6 were conducted utilizing a standard parent I-section beam (IPE140) as the control specimen. The test findings include the ultimate load vs. mid-span deflection response curves and failure mechanisms. The testing findings indicated that the TCBs' ultimate load capacity might be up to 140 percent of that of the parent section. The Abaqus program was used to conduct a finite element (FE) analysis of TCB, which allows for material and geometric nonlinearity. The derived finite element models exhibit excellent agreement with the experimental results in terms of ultimate load capacity vs. mid-span deflection response and failure mechanisms. Based on the results of the work, TCBs can be used for increasing the strength and stiffness of the I-section parent beam with adding expansion plates. The maximum load capacity of TCBs can be enhanced when adding expansion plates up to 40 % above that of the parent beam. A TCB has lower ductility than its parent beam. Moreover, a TCB fulfills serviceability requirements since its mid-span depth exceeds that of its parent beam.

Theory toolbox for historical explanation: An essay in analytic sociology

Merton proposed middle range theories, not as ends in themselves, but as bases for a consolidation to explain broader phenomenon. More than a half century has passed since Merton’s consolidation proposal and in that time a number of experimentally tested middle range theories have been developed. Certainly, the next step should be a consolidation. Yet, to our knowledge, no one has previously offered a consolidation of experimentally tested theories and applied it for explanation. This paper offers a consolidation of middle range theories formulated to explain the rise of the pristine state. Two theories of this consolidation, Status Characteristics Theory and Elementary Theory, form the core of what Analytic Sociologists have called a toolbox of theories. Our toolbox forms an integrated consolidation in two ways. First, the social structures modeled by the theories form a path-dependent process of increasing benefits gained by the elites of the structures. Second, the end conditions of each step of the process are the initial conditions of the next. Whereas the theories in our toolbox have previously been seen as applying exclusively to microstructures, we have encountered no difficulties in scaling them up to apply to macrostructures. While we hope the consolidation has validity in explaining the occurrence of pristine states, this paper’s significance lies in its demonstration that today social theories can be consolidated and applied for explanation.