Structural Mechanics Method Research Articles

Research on rational layout of strut arms of tainter gate in vertical frame

The overall stability of hydraulic tainter steel gate decrease seriously, and they are caused by improper structure layout of the two-way eccentric compression of struts. Chinese and American specification method, structural mechanics method and finite element method are respectively used to study rational structural layout of strut arms in vertical frame. First of all, a unified method for rational layout of struts of tainter gate in vertical frame is deduced by using structural mechanics method that simplifies curve girder as straight girder on the basis of zero rotation in vertical girder. Second, rational layouts of struts were researched by utilizing spatial finite element method according to zero rotation in vertical girder. The 756 groups rational layout results of the above three methods with different water heads, different number of struts and different unit stiffness ratios were researched. The differences of struts stress and material dosages of various rational layout methods were evaluated. From the point of view of the forces of tainter gate struts in vertical frame, as the results shown, the layouts of struts by Chinese and American specification method, straight beam method and finite element method are large eccentric compression, small eccentric compression and axial compression respectively. The layout of struts with specification method in lower head is quite different from straight beam method and finite element method, and the layouts of deep water head with straight beam method and finite element method are tend to be consistent. Unit stiffness ratio between vertical girder and strut has little effect on layout of tainter gate struts, but has a great influence on material dosages of tainter gate. Compared with specification method, layout of tainter gate with two struts and three struts by using straight beam method and finite element method can improve stability of struts and save materials of overall tainter gate structure, and the material saving rates of tainter gate with two struts and three struts with finite element method are respectively [32.63, 47.58] (%) and [21.61, 30.01] (%). Rational layout concise charts of tainter gate with two struts and three struts by specification method, straight beam method and finite element method are given, which can be used directly for projects designs. Compared with specification method, the layout of struts of straight beam method and finite element method is not only security and economy, but also method and mechanics concept are simple, which can provide the theoretical basis for specification revision of Chinese and American.

TENSION AND DEFORMATIONS OF STAR-SHAPED SPRING VERTICES WITH STRANGULATED ENDS OF THE FLEXIBLE COUPLING

The article examines the structure of overload flexible coupling that contains internal and external hubs, connected by a star-shaped spring with the circular vertices inserted in grooves on the outer surface of internal hub and inner surface of the external hub. Position of the star-shaped spring is fixed on the inner hub by the wedge, which allows the spring to be made either solid or of separate circular vertices with strangulated ends. Geometric synthesis of star-shaped spring with vertices of circular shape, depending on its size was conducted. It is assumed that star spring vertices are the double-hinge arches of circular form. Calculations of analytical solutions using the methods of structural mechanics were done. Analytical expressions proved workability of the star-shaped spring of flexible overload coupling during the torque transmission.

Calculating Mechanics Characteristics of Single-Walled Carbon Nanotube Materials by Finite Element Method

In this paper, we establish the mechanical property analysis of Single-walled Carbon Nanotubes (SWCNTs) modified beam element model based on the molecular structural mechanics method. Then we study the mechanical properties of their radial direction characteristics using the finite element software Abaqus. The model simulated the different bending stiffness with rectangular section beam elements C-C chemical force field. When the graphene curled into arbitrary chirality of SWCNTs spatial structure, the adjacent beam position will change the moment of inertia of the section of the beam. Compared with the original beam element model and the calculation results, we found that the established model largely reduced the overestimate of the original model of mechanical properties on the radial direction of the SWCNTs. At the same time, compared with other methods available in the literature results and the experimental data, the results can be in good agreement.

Analysis of displacements in beam structures and shells with middle developable surfaces

Generally the displacements of the beams are calculated by the traditional methods of structural mechanics with the help of approximate formulas which provide good results for linear tasks. The author shows that the approximate formula is not suitable for analysis in the case of geometrical nonlinearity which occurs during the manufacturing process of bending developable shells. The comparison of results got by methods of structural mechanics and shell theory for the shells with developable middle surfaces is given.

INFORMATION EDUCATIONAL TECHNOLOGIES IN THE STUDY OF THE DISCIPLINES OF STRENGTH CYCLE

This article considers the current state of the higher education system of the Russian Federation in the context of teaching disciplines of strength cycle with the use of information educational technologies. The educational process in the discipline «Structural Mechanics» is shown by using the Controlling-Training Software on the sample program "Statically Determinate Plane Truss". Such software makes it possible not only to consolidate but also to independently assess the acquired theoretical knowledge. The Controlling-Training Software was developed by employees of the Department of Structural Mechanics of the Institute of Architecture and Civil Engineering of Volgograd State Technical University to heighten student's interest in calculations of building structures while using computer-based teaching methods, as well as to simplify the existing monitoring procedure. The use of vivid visuals and interactive hints can significantly simplify the process of perception of the theoretical material and to a large extent to promote the features of calculations of building structures using methods of structural mechanics.

Crack Identification in Graphene Using Eigenfrequencies

Graphene, due to its remarkable properties, is expected to be a key element for nanomachines and nanoelectromechanical systems (NEMs). Progressively, research on graphene should be shifted from property characterization towards reliability performance. In this context, an initial effort is made here to establish a diagnostic technique, capable of detecting the size and the position of a straight crack in graphene. The formulation is grounded on the fact that the presence of a crack in graphene has a significant impact on its vibration behavior. Not only the crack size but also the position of the crack influences the eigenbehavior of graphene. Hence, in the present study, the free vibration of a cracked and an uncracked graphene sheet of the same size is simulated to compute the first three natural frequencies as well as to calculate the corresponding frequency changes. The simulations are realized by adopting an efficient, atomistic, three-dimensional, spring-based, structural mechanics method. Numerous crack sizes and locations and two representative crack orientations are investigated. Validation of the adopted numerical approach is preceded through comparisons with relevant data found in the literature, regarding the free vibration of pristine graphene. Then, the diagrams of the arisen natural frequency shifts due to the crack are appropriately superposed in common contour maps to enable simple crack identification, i.e., detection of the crack length and position, from contour intersections.

Розрахунок військового низьководного мосту на горизонтальне навантаження

Проведено дослідження роботи дерев’яної мостової споруди при дії гальмівних навантажень. Під час будівництва військових низьководних мостів та при подальшій їх експлуатації проводились експериментальні дослідження роботи конструкції елементів мосту на дію горизонтальних навантажень. На підтвердження експериментальних досліджень були проведені розрахунки конструктивних систем мосту, що зводились до розрахунків багатоконтурних плоских рам на основі методів будівельної механіки. З’ясовано, що при початковій дії навантаження на одному з прольотів мосту зусилля сприймаються лише двома сусідніми рядами опор мосту. Коли величина горизонтального переміщення становила 4 см і більше, в роботу включалися наступні суміжні ряди опор конструкції мосту.

In Memoriam: Dr. Clive L. Dym (1942–2016)

In Memoriam: Dr. Clive L. Dym (1942–2016)

The aeroelastic characteristics of high aspect ratio wing

Owing to the elasticity, the large deformation was brought in the high aspect ratio wing in the flight. The large deformation had a great influence on the flight performance. In this paper, the loosely coupled method was used for the research of high aspect ratio wing aeroelastic problems. The Navier–Stokes equations were solved for fluid domain computation, and the nonlinear finite element method was adopted for solid domain computation. The data exchange program and mesh regeneration progress were adopted for fluid–structure interface problem. Finally, the aerodynamic characteristics of high aspect ratio wing were obtained under different fly conditions. In addition, to validate the proposed method, the flutter analysis of AGARD 445.6 wing is carried out and compared with the experimental data. The numerical result validates the proposed computational fluid dynamics/computational structural mechanics method.

An improved molecular structure mechanics method and its application for graphene wrinkling

This paper proposes an improved molecular structure mechanics (iMSM) method to study the wrinkling characteristics of annular graphene sheet (AGS). An idea of variable cross-section beam, combined with 3-node Timoshenko beam, is introduced in the iMSM model for considering the flexibility of C-C bond and C-C joint simultaneously, and the stiffness matrix of beam element is deduced for later calculation. The parameters of equivalent beam are obtained by using an interior point optimization approach. Based on the proposed iMSM model, the wrinkling characteristics of AGS are simulated, which are verified by molecular dynamic (MD) simulation. A predicted model is used to evaluate the wrinkling level of AGS, which agrees well with the iMSM simulation, and then the effects of beam parameters on graphene wrinkling are also analyzed. The results indicate that our proposed model is reliable to the wrinkling analysis of AGS and may be further used for other researches on graphene.

The influence of tilt grain boundaries on the mechanical properties of bicrystalline graphene nanoribbons

The mechanical properties of bicrystalline graphene nanoribbons with various tilt grain boundaries (GBs) which typically consist of repeating pentagon–heptagon ring defects are investigated based on the method of molecular structural mechanics. The GB models are constructed via the theory of disclinations in crystals, and the elastic properties and ultimate strength of bicrystalline graphene nanoribbons are calculated under uniaxial tensile loads in perpendicular and parallel directions to grain boundaries. The dependence of mechanical properties is analyzed on the chirality and misorientation angles of graphene nanoribbons, and the experimental phenomena that Young's modulus and ultimate strength of bicrystalline graphene nanoribbons can either increase or decrease with the grain boundary angles are further verified and discussed. In addition, the influence of GB on the size effects of graphene Young's modulus is also analyzed.

Vibration analysis of defective graphene based on the molecular structural mechanics method

A molecular structural mechanics method has been implemented to investigate the vibrational characteristics of single-layer graphene (SLG) with defects. By adopting the lumped mass unit to replace carbon atoms, and the beam element with circular cross-section to mimic C–C covalent bonds, SLG is modeled as a space framework. The simulation results show that the chirality almost has no effect on the natural frequency and the vibration mode of SLG, while boundary conditions have great influences. The influences of defects with different number and location on the natural frequencies are also studied. It is concluded that vibration mode is insensitive to the vacancy defect, small hole and short flaw, but large holes and long flaws can affect the vibration characteristics. So the graphene sheet even with small defect effects might be selected as the nanosensor material as well as pristine graphene. The conclusions in this paper may provide some references for the design of nanosensor.

Laser speckle based digital optical methods in structural mechanics: A review

Laser Speckle Correlation, Electronic Speckle Pattern Interferometry and Digital Holographic interferometry have evolved for decades to become relevant techniques in many fields of today’s wide spectrum of knowledge and disciplines. Indeed, with today׳s advances in optics, photonics, electronics and computing there are many important applications for them and strictly speaking there are an almost infinite number of applications that one can think of, as they are non-contact optical techniques that can be used to measure mechanical parameters ranging from a few microns to hundreds of nanometers. In this review we will explore and discuss some relevant applications in structural mechanics in the fields of materials in engineering, biomedical and art preservation and restoration. This work will take the reader from a succinct historical account on the development of these techniques, followed by a brief theoretical description for each one that will then facilitate the introduction of the results chosen as the key applications, ending the review with the conclusions. From the myriad of papers now available in the web, we will only present those that we believe are the most illustrative applications within three lustrum, 2000 to 2015, all set to give a frame that place these optical techniques as mature technologies with an absolute relevance to conduct metrology in many fields.

Synthesis of the force and displacement methods of structural mechanics. The planar truss case

The papers delivers a new computational method of statical analysis of frames, well suited for both the 2D and 3D settings and easily generalizable to the case of the presence of big axial forces. The method is based on the compatibility equations which have their roots in the force method, while the unknowns refer to the displacement method. These equations involve also the unknown cross sectional forces which are the force method unknowns. The method proposed can be viewed as the displacement method with an implicit procedure of deriving the stiffness equations.

A modified molecular structure mechanics method for analysis of graphene

Based on molecular mechanics and the deformation characteristics of the atomic lattice structure of graphene, a modified molecular structure mechanics method was developed to improve the original one, that is, the semi-rigid connections were used to model the bond angle variations between the C-C bonds in graphene. The simulated results show that the equivalent space frame model with semi-rigid connections for graphene proposed in this article is a simple, efficient, and accurate model to evaluate the equivalent elastic properties of graphene. Though the present computational model of the semi-rigid connected space frame is only applied to characterize the mechanical behaviors of the space lattices of graphene, it has more potential applications in the static and dynamic analyses of graphene and other nanomaterials.

Free vibration analysis of microtubules based on the molecular mechanics and continuum beam theory.

A molecular structural mechanics (MSM) method has been implemented to investigate the free vibration of microtubules (MTs). The emphasis is placed on the effects of the configuration and the imperfect boundaries of MTs. It is shown that the influence of protofilament number on the fundamental frequency is strong, while the effect of helix-start number is almost negligible. The fundamental frequency is also found to decrease as the number of the blocked filaments at boundaries decreases. Subsequently, the Euler-Bernoulli beam theory is employed to reveal the physics behind the simulation results. Fitting the Euler-Bernoulli beam into the MSM data leads to an explicit formula for the fundamental frequency of MTs with various configurations and identifies a possible correlation between the imperfect boundary conditions and the length-dependent bending stiffness of MTs reported in experiments.

A modified molecular structural mechanics model for the buckling analysis of single layer graphene sheet

Abstract In this paper the classical molecular structural mechanics model of graphene is modified to improve its accuracy for the analysis of transverse deformations. To this aim, a sample graphene sheet under a uniform pressure is modeled by both molecular dynamics and molecular structural mechanics methods. The sectional properties of the beam element, by which the covalent bonds are modeled, are modified such that the difference between the results of the molecular mechanics model and molecular dynamics simulation is minimized. Using this modified model, the buckling behavior of graphene under a uniform edge pressure is investigated subjected to different boundary conditions for both zigzag and armchair chiralities. The results show that the obtained buckling loads are considerably less than those reported using the classical molecular structural models in the literature.

Accurate modelling of flow induced stresses in rigid colloidal aggregates

A method has been developed to estimate the motion and the internal stresses induced by a fluid flow on a rigid aggregate. The approach couples Stokesian dynamics and structural mechanics in order to take into account accurately the effect of the complex geometry of the aggregates on hydrodynamic forces and the internal redistribution of stresses. The intrinsic error of the method, due to the low-order truncation of the multipole expansion of the Stokes solution, has been assessed by comparison with the analytical solution for the case of a doublet in a shear flow. In addition, it has been shown that the error becomes smaller as the number of primary particles in the aggregate increases and hence it is expected to be negligible for realistic reproductions of large aggregates.The evaluation of internal forces is performed by an adaptation of the matrix methods of structural mechanics to the geometric features of the aggregates and to the particular stress–strain relationship that occurs at intermonomer contacts. A preliminary investigation on the stress distribution in rigid aggregates and their mode of breakup has been performed by studying the response to an elongational flow of both realistic reproductions of colloidal aggregates (made of several hundreds monomers) and highly simplified structures. A very different behaviour has been evidenced between low-density aggregates with isostatic or weakly hyperstatic structures and compact aggregates with highly hyperstatic configuration. In low-density clusters breakup is caused directly by the failure of the most stressed intermonomer contact, which is typically located in the inner region of the aggregate and hence originates the birth of fragments of similar size. On the contrary, breakup of compact and highly cross-linked clusters is seldom caused by the failure of a single bond. When this happens, it proceeds through the removal of a tiny fragment from the external part of the structure. More commonly, however, breakup takes place through a sequence of bond failures that start at the periphery of the aggregates and then moves toward the interior according to a crack propagation mechanism. A gradual transition between these two modes of breakup has been found as the density of the aggregates increases.

ANALISIS DE LAS VIBRACIONES DE SISTEMAS DE RIGIDEZ NO LINEAL MEDIANTE EL CALCULO FRACCIONARIO

A dynamical analysis of nonlinear structural systems by means of fractional calculus is presented. The reason for this study is to find an alternative to methods like Runge-Kutta which duplicate the number of equations to solve. The aim is, then, to linearize the system of equations and apply traditional methods in structural mechanics keeping the size of the system, like the finite central difference method. The proposed methodology transforms the original nonlinear problem into a fractional integro-differential equation, in which the fractional operator represents a variable stiffness. Two typical cases of application in mechanical engineering are presented: the elastic impact of two spheres (system of one degree of freedom) and the transient dynamic response of a building (system of multiples degrees of freedom). It is concluded from the obtained results that the proposed method describes correctly the response of the studied systems, reducing the computational cost.

Buckling of microtubules: An insight by molecular and continuum mechanics

The molecular structural mechanics method has been extended to investigate the buckling of microtubules (MTs) with various configurations. The results indicate that for relative short MTs the shear deformation effect, rather than the nonlocal effect, is mainly responsible for the limitation of their widely used Euler beam description and the observed length-dependence of their bending stiffness. In addition, the configuration effect of MTs is also studied and considered as an explanation for the large scattering of the critical buckling force and bending stiffness observed in existing experiments. This configuration effect is also found to mainly originate from the geometry of the MTs and is mainly determined by the protofilament number.