Fig 5 - uploaded by Sushanta Ghuku
Content may be subject to copyright.
Source publication
The paper presents experimental and theoretical large deflection analysis of non-uniformly curved beam with moving boundaries under static loading within elastic domain. A master leaf spring is considered as physical model of the curved beam problem and its load–deflection behaviour is studied experimentally in a specially designed testing rig. Bes...
Context in source publication
Context 1
... body diagram of the right roller is similar to that of the left roller and hence it is not shown, but locations of points B, B 0 and B 1 and corresponding angles w R and w 0 R are shown in Fig. 5(a). In case of the right roller, normal and tangential com- ponents of reaction force R R at B 0 are indicated by N R and T R respec- tively. Similarly, horizontal and vertical components of R R are indicated by P xR and P yR , where P yR ¼ R yR and P xR ¼ R R cos w 0 R . The roller supports of the physical system are eliminated to obtain ...
Similar publications
Mobile networks, constructed with simple linkages by tessellation, have great application potential in engineering as they could change their shapes according to the need of working state by one degree of freedom (DOF). However, the existing one-DOF networks are always composed of bar-like links, and cooperated membranes should be designed and fabr...
This paper proposes a volumetric accuracy enhancement method of rotary axes in five-axis machine tools through constructing equivalent rotary axis (ERA). The influences of translational axes, setup errors of table ball and tool ball are simultaneously considered. A new concept named ERA, originated from the definition of axis of rotation, is propos...
![Fig. 6. Stress distribution in the specimen with layup [0°/90°] 12 and...](publication/349473816/figure/fig3/AS:993499293954048@1613880098595/Stress-distribution-in-the-specimen-with-layup-0-90-12-and-6-mm-crack-after_Q320.jpg)
![Fig. 11. Fatigue curve for material AS/8552 [28]](publication/349473816/figure/fig5/AS:993499293954049@1613880098862/Fatigue-curve-for-material-AS-8552-28_Q320.jpg)
The problem of deformation and elastoplastic buckling of shells of revolution with a thick-walled elastic core under combined static and dynamic loading is formulated in a two-dimensional planar formulation based on two approaches: full-scale modeling within the framework of continuum mechanics and a simplified formulation based on the hypotheses o...
The wave-based method (WBM) is a feasible method which investigates the free vibration characteristics of orthotropic cylindrical shells under general boundary conditions. Based on Reissner–Naghid’s shell theory, the governing motion equation is established, and the displacement variables are transformed into wave functions formed to satisfy the go...
In order to complete the processing of large-scale workpieces, a region division of large-scale workpieces based on robot dexterous workspace is studied. The linkage coordinate system of the robot is established by D-H method, and the forward kinematics equation of the robot is obtained; Monte Carlo method is used to analyze the workspace of the ro...
Citations
... Numerous researchers have proposed various techniques in various studies to investigate the magnitude of stresses and deflections in curved beams under various loading situations [4][5][6]. While many research studies took into account bending and stretching simultaneously, for instance [7,8]. ...
... Lacarbonara et al. (2005 investigated a two-mode activated around a veering of the frequencies of the lowest two modes due to nonlinear stretching of the imperfect beams. Pre/postbuckling, bending and vibration behaviors of composite beams with and without imperfections have been reported by many authors (Gupta et al. 2010, Gunda et al. 2011, Alazwari et al. 2021, Emam et al. 2018, Ghuku and Saha 2018, Guo et al. 2019, Melaibari et al. 2021, Hamed et al. 2020a, Abo-bakr et al. 2021, Emam and Lacarbonara 2021, She 2020, Zhang et al. 2021a, Assie et al. 2022. ...
This manuscript presents a comprehensive mathematical model to investigate buckling stability and postbuckling response of bio-inspired composite beams with helicoidal orientations. The higher order shear deformation theory as well as the Timoshenko beam theories are exploited to include the shear influence. The equilibrium nonlinear integro-differential equations of helicoidal composite beams are derived in detail using the energy conservation principle. Differential integral quadrature method (DIQM) is employed to discretize the nonlinear system of differential equations and solve them via the Newton iterative method then obtain the response of helicoidal composite beam. Numerical calculations are carried out to check the validity of the present solution methodology and to quantify the effects of helicoidal rotation angle, elastic foundation constants, beam theories, geometric and material properties on buckling, postbuckling of bio-inspired helicoidal composite beams. The developed model can be employed in design and analysis of curved helicoidal composite beam used in aerospace and naval structures.
... In the current bottom-up semi-analytical framework for estimation of the elastic failure strength of anti-curvature lattices, we first focus on the nonlinear deformation and stress physics at the beam-level [58][59][60] considering anti-curvature in the beam profile, and thereby the stress and deformation results are subsequently used at the next level to evaluate the elastic failure strength of the entire lattice following a unit cell-based approach. It can be noted that slender curved beam-like 8 cell walls involve initial curvature and undergo large deformation before reaching the yield state. ...
Over the last decade, lattice-based artificial materials have demonstrated the possibility of tailoring multifunctional capabilities that are not achievable in traditional materials. While a large set of mechanical properties can be simultaneously modulated by adopting an appropriate network architecture in the conventional periodic lattices, the prospect of enhancing global specific stiffness and failure strength has become rather saturated lately due to intense investigation in this field. Thus there exists a strong rationale for innovative design at a more elementary level in order to break the conventional bounds of specific stiffness and failure strength that can be obtained only by lattice-level geometries. Here we propose a novel concept of anti-curvature in the design of lattice materials, which reveals a dramatic capability in terms of enhancing the elastic failure strength in the nonlinear regime while keeping the relative density unaltered. A semi-analytical bottom-up framework is developed for estimating the onset of failure in honeycomb lattices with the anti-curvature effect in cell walls considering geometric nonlinearity under large deformation. The physically insightful semi-analytical model captures nonlinearity in elastic failure strength of anti-curvature lattices as a function of the degree of curvature and applied stress together with conventional microstructural and intrinsic material properties.
... Such conguration of a unit cell involving the pro-curvature eect is shown in Figure 1 This section uses a bottom-up semi-analytical framework to estimate the eective nonlinear shear modulus of anti-curvature lattices. We rst consider the nonlinear deformation physics at the beam level, considering curvature in the prole [62,63]. Based on the unit cell approach, the deformation results are used on the entire lattice in the subsequent steps to evaluate the eective shear modulus. ...
Shear modulus assumes an important role in characterizing the applicability of different materials in various multi-functional systems and devices such as deformation under shear and torsional modes, and vibrational behaviour involving torsion, wrinkling and rippling effects. Lattice-based artificial microstructures have been receiving significant attention from the scientific community over the past decade due to the possibility of developing materials with tailored multifunctional capabilities that are not achievable in naturally occurring materials. In general, the lattice materials can be conceptualized as a network of beams with different periodic architectures, wherein the common practice is to adopt initially straight beams. While shear modulus and multiple other mechanical properties can be simultaneously modulated by adopting an appropriate network architecture in the conventional periodic lattices, the prospect of on-demand global specific stiffness and flexibility modulation has become rather saturated lately due to intense investigation in this field. Thus there exists a strong rationale for innovative design at a more elementary level in order to break the conventional bounds of specific stiffness that can be obtained only by lattice-level geometries. In this article, we propose a novel concept of anti-curvature in the design of lattice materials, which reveals a dramatic capability in terms of enhancing shear modulus in the nonlinear regime while keeping the relative density unaltered. A semi-analytical bottom-up framework is developed for estimating effective shear modulus of honeycomb lattices with the anti-curvature effect in cell walls considering geometric nonlinearity under large deformation. We propose to consider the complementary deformed shapes of cell walls of honeycomb lattices under anti-clockwise or clockwise modes of shear stress as the initial beam-level elementary configuration. A substantially increased resistance against deformation can be realized when such a lattice is subjected to the opposite mode of shear stress, leading to increased effective shear modulus. Within the framework of a unit cell based approach, initially curved lattice cell walls are modeled as programmed curved beams under large deformation. The combined effect of bending, stretching and shear deformation is considered in the framework of Reddy’s third order shear deformation theory in a body embedded curvilinear frame. Governing equation of the elementary beam problem is derived using variational energy principle based Ritz method. In addition to application-specific design and enhancement of shear modulus, unlike conventional materials, we demonstrate through numerical results that it is possible to achieve non-invariant shear modulus under anti-clockwise and clockwise modes of shear stress. The developed physically insightful semi-analytical model captures nonlinearity in shear modulus as a function of the degree of anti-curvature and applied shear stress along with conventional parameters related to unit cell geometry and intrinsic material property. The concept of anti-curvature in lattices would introduce novel exploitable dimensions in mode-dependent effective shear modulus modulation, leading to an expanded design space including more generic scopes of nonlinear large deformation analysis.
... In the current bottom-up semi-analytical framework for estimation of the effective nonlinear elastic properties of anti-curvature lattices, we first focus on the nonlinear deformation physics at the beam-level [48,49] considering anti-curvature in the beam profile, and thereby the results are subsequently used at the next level to evaluate the effective properties of the entire lattice following 7 a unit cell-based approach. Here the mathematical formulation of honeycomb lattice with anticurvature effect is developed for initially stretched configuration under compressive loading mode along both directions (1 and 2), as shown in Figure 1(e-4) and (f-4). ...
Lattice-based artificial microstructures have been receiving significant attention from the scientific community over the past decade due to the possibility of developing materials with tailored multifunctional capabilities that are not achievable in naturally occurring materials. Such lattice materials can be conceptualized as a network of beams with different periodic architectures, wherein the common practice is to adopt straight beams. While a large set of mechanical properties can be simultaneously modulated by adopting an appropriate network architecture in the conventional periodic lattices, the prospect of on-demand global specific stiffness and flexibility modulation has become rather saturated lately due to intense investigation in this field. Thus there exists a strong rationale for innovative design at a more elementary level in order to break the conventional bounds of specific stiffness that can be obtained only by lattice-level geometries. Here we propose a novel concept of anti-curvature in the design of lattice materials, which reveals a dramatic capability in terms of enhancing the effective elastic moduli in the nonlinear regime while keeping the relative density unaltered. A semi-analytical bottom-up framework is developed for estimating effective elastic moduli of honeycomb lattices with the anti-curvature effect in cell walls considering geometric nonlinearity under large deformation. We propose to consider the deformed shapes corresponding to compressive or tensile modes of the honeycomb cell walls as the initial beam-level configuration. A substantially increased resistance against deformation can be realized when such a lattice is subjected to the opposite mode, leading to increased effective elastic moduli. Moreover, unlike conventional materials, we demonstrate that it is possible to achieve non-invariant elastic moduli under tension and compression. Within the framework of a unit cell based approach, the cell walls with initial curvature are modeled as curved beams including nonlinear bending and axial deformation, wherein the governing equation is derived using variational energy principle through the Ritz method. The developed physically insightful semi-analytical model captures nonlinearity in elastic moduli as a function of the degree of anti-curvature and applied stress along with conventional parameters related to unit cell geometry and intrinsic material property. The concept of anti-curvature in lattice materials proposed in the present article introduces novel exploitable dimensions in mode-dependent effective elastic property modulation, leading to an expanded design space including more generic scopes of nonlinear large deformation analysis.
... To decode what type of beam to be used in a structure depends upon the loading system and its potential deflection. Deflection is the displacement of any point or part of beam from its original position, measured in y-direction [7]. The specific values of deflection for a given load can be found through differential equation [13]. ...
... Batista [2] used the general solution to derive an approximate formula that provides an explicit relation between the beam load and its midpoint deflection. Ghuku and Saha [7] solved the nonlinear governing equation numerically using Lagrangian approach, and compared the results with experimental work. The study of the modelling of a beam and its parameter analysis plays significant role in the field of mechanical, aerospace and civil engineering. ...
... Since e r x 0, r 2 + n 2 = 0, so that r = i n, where i = -1 . So, complementary function [6] is yc (x) = c1 cos nx + c2 sin nx, and particular integral [7] is ...
In this paper, we present the model equation of a beam when it applies compression forces on ends of the beam and carries a load. For the structural point of view, there should be a suitable model to understand the behavior under different conditions of loading of a beam. Mathematical modeling is the simulation of a physical structure or physical phenomenon by constructing suitable analytic and numerical solution. We analyze the deflections of the beam by taking different structures of beam. The structures of beam depend on the compression forces on beams with different beams with different weights. We observe the deflection by applying various compression forces at the ends of the beam. The influence of the effect of some parameters appeared in mathematical formulations such as area moment of inertia (I), Young’s modulus (E), load (W) and compressive force (P) on deflection variation are investigated in this paper. We analyze the results that how compression forces affect the system. We use finite difference method to solve the model equation numerically. We analyze and compare the numerical result with analytic solution. BIBECHANA 18 (2021) 75-82
... Using a special purpose AutoLISP® code, these points are saved in an MS Excel® file for each setting under respective loading. Detailed description of the image processing technique used here to obtain loaded beam elastica may be found elsewhere [2,30]. The MS Excel® files are imported into MATLAB® and deflection profiles of beam under each loaded condition are plotted and shown in Fig. 6. ...
The present paper reports an experimental study on the effect of finite clamping on static and dynamic characteristics of cantilever beam. The experiment is carried out with two different beams, each of which is clamped at two different locations resulting in two different geometry settings. Under each of these four settings, specimen is clamped under two different torque ratings giving rise to different finite clamping effect. Under the eight settings, coordinates of tip point under static loading are measured directly using scales and plumb at each load step; whereas, complete deflection profiles of loaded beam under each static load step are obtained through post-processing of images captured during experimentation. Such image processing is carried out manually using AutoCAD ® and in-built AutoLISP ® software. Strain measurements at each static load step are carried out by using strain gauge, a universal data acquisition system and the associated Catman Easy ® software. To obtain loaded free vibration characteristics, loaded beam under each setting is disturbed by a rubber hammer and its dynamic response is recorded from strain gauge signal through Catman Easy ® software. These dynamic strain readings of loaded beam are post-processed and FFT plots are generated in MATLAB ® software and first two loaded natural frequencies of beam under each setting are obtained. Finally, effects of clamping torques on the static strain and deflection results and loaded natural frequencies for beam settings with the four different thickness to length ratios are reported in a suitable manner. The result reported may be useful as ready reference to develop a theoretical model of clamped beam like structures incorporating the effect of finite clamping.
... Using a special purpose AutoLISP® code, these points are saved in an MS Excel® file for each setting under respective loading. Detailed description of the image processing technique used here to obtain loaded beam elastica may be found elsewhere [2,30]. The MS Excel® files are imported into MATLAB® and deflection profiles of beam under each loaded condition are plotted and shown in Fig. 6. ...
The present paper reports an experimental study on the effect of finite clamping on static and dynamic characteristics of cantilever beam. The experiment is carried out with two different beams, each of which is clamped at two different locations resulting in two different geometry settings. Under each of these four settings, specimen is clamped under two different torque ratings giving rise to different finite clamping effect. Under the eight settings, coordinates of tip point under static loading are measured directly using scales and plumb at each load step; whereas, complete deflection profiles of loaded beam under each static load step are obtained through post-processing of images captured during experimentation. Such image processing is carried out manually using AutoCAD ® and in-built AutoLISP ® software. Strain measurements at each static load step are carried out by using strain gauge, a universal data acquisition system and the associated Catman Easy ® software. To obtain loaded free vibration characteristics, loaded beam under each setting is disturbed by a rubber hammer and its dynamic response is recorded from strain gauge signal through Catman Easy ® software. These dynamic strain readings of loaded beam are post-processed and FFT plots are generated in MATLAB ® software and first two loaded natural frequencies of beam under each setting are obtained. Finally, effects of clamping torques on the static strain and deflection results and loaded natural frequencies for beam settings with the four different thickness to length ratios are reported in a suitable manner. The result reported may be useful as ready reference to develop a theoretical model of clamped beam like structures incorporating the effect of finite clamping.
Theoretical and experimental large deflection and stress analysis of a master leaf spring considering stress concentration effect of clamping is reported. The non-uniformly curved master leaf spring under three point bending subjected to moving boundaries is modeled. Geometrically nonlinear strain-displacement relations, as necessary for the theoretical analysis, are derived through visualization of physics behind the large deformation problem. An embedded curvilinear coordinate system is considered, to study the combined effects of non-uniform curvature, bending, stretching and shear deformation including cross-sectional warping. Governing equation of the non-uniformly curved beam system is derived in variational form using energy method, based on linear material constitutive relations and the derived nonlinear kinematic relations. An iterative solution scheme through successive geometry updation is developed and executed in MATLAB ® software to solve the governing equation involving strong geometric nonlinearity together with complicating moving boundary effect. Experimental deflection profiles under static loading are obtained through manual image processing technique using AutoCAD ® software. Whereas, strain measurements are performed using strain gauges with data acquisition system (HBM-MX840B). Comparison between the theoretical and experimental results lead towards observation on stress concentration effect due to presence of geometric discontinuity in form of a small hole in the physical system. A modified formulation is proposed using domain decomposition method incorporating effect of geometric discontinuity through an equivalent curved beam geometry of variable cross-section. The modified theoretical model is validated successfully with the experimental results, and observations on stress characteristics and effect of hole diameter to beam width ratio are made.
The present study aims to formulate strain energy release rates (SERR) for curved beams, which are supposed to be cut from tanks or cylinders, in End-Notched Flexure (ENF) tests based on Euler-Bernoulli’s and Timoshenko’s curved beam theories. The derived SERRs based on the curved beam theories were compared with those based on the flat beam theory for specimens with various geometries to prove the validity of using the curved beam theory in the ENF tests of curved beams. The validity of the derived compliance and SERRs was verified for the specimens with various geometries using a two-dimensional finite element analysis, in which virtual crack closure techniques were used to calculate the SERRs. The results revealed that Euler–Bernoulli’s curved beam theory was effective in cases with large radius-of-curvature-to-thickness (R/h) values but not in those with small R/h values, whereas Timoshenko’s curved beam theory was effective even for small R/h values.
