Free vibration and buckling analysis of polymeric composite beams reinforced by functionally graded bamboo fbers

Natural fibers have been extensively researched as reinforcement materials in polymers on account of their environmental and economic advantages in comparison with synthetic fibers in the recent years.Bamboo fibers are renowned for their good mechanical properties,abundance,and short cycle growth.As beams are one of the fundamental structural components and are susceptible to mechanical loads in engineering applications,this paper performs a study on the free vibration and buckling responses of bamboo fiber reinforced composite(BFRC)beams on the elastic foundation.Three different functionally graded(FG)layouts and a uniform one are the considered distributions for unidirectional long bamboo fibers across the thickness.The elastic properties of the composite are determined with the law of mixture.Employing Hamilton’s principle,the governing equations of motion are obtained.The generalized differential quadrature method(GDQM)is then applied to the equations to obtain the results.The achieved outcomes exhibit that the natural frequency and buckling load values vary as the fiber volume fractions and distributions,elastic foundation stiffness values,and boundary conditions(BCs)and slenderness ratio of the beam change.Furthermore,a comparative study is conducted between the derived analysis outcomes for BFRC and homogenous polymer beams to examine the effectiveness of bamboo fibers as reinforcement materials,demonstrating the significant enhancements in both vibration and buckling responses,with the exception of natural frequencies for cantilever beams on the Pasternak foundation with the FG-◇fiber distribution.Eventually,the obtained analysis results of BFRC beams are also compared with those for carbon nanotube reinforced composite(CNTRC)beams found in the literature,indicating that the buckling loads and natural frequencies of BFRC beams are lower than those of CNTRC beams.

用于抵抗扭转采取边缘弹性约束下的单轴压缩下板材极限强度:一种新的综合方法

The ultimate strength of platings under compression is one of the most important factors to be addressed in the ship design.Current Rules for ship structural design generally provide explicit strength check criteria against buckling for simply supported and clamped platings.Nevertheless,ship platings generally exhibit an intermediate behaviour between the simple support and the clamped conditions,which implies that the torsional stiffness of supporting members should be duly considered.Hence,the main aim of this study is the development of new design formulas for the ultimate strength of platings under uniaxial compression,with short and/or long edges elastically restrained against torsion.In this respect,two benchmark studies are performed.The former is devoted to the development of new equations for the elastic buckling coefficients of platings with edges elastically restrained against torsion,based on the results of the eigenvalue buckling analysis,performed by Ansys Mechanical APDL.The latter investigates the ultimate strength of platings with elastically restrained edges,by systematically varying the plate slenderness ratio and the torsional stiffness of supporting members.Finally,the effectiveness of the new formulation is checked against a wide number of finite element(FE)simulations,to cover the entire design space of ship platings.

Mixed finite element and differential quadrature method for free and forced vibration and buckling analysis of rectangular plates

This paper presents a combined application of the finite element method （FEM） and the differential quadrature method （DQM） to vibration and buckling problems of rectangular plates. The proposed scheme combines the geometry flexibility of the FEM and the high accuracy and efficiency of the DQM. The accuracy of the present method is demonstrated by comparing the obtained results with those available in the literature. It is shown that highly accurate results can be obtained by using a small number of finite elements and DQM sample points. The proposed method is suitable for the problems considered due to its simplicity and potential for further development.

Buckling analysis of functionally graded material(FGM) sandwich truncated conical shells reinforced by FGM stiffeners filled inside by elastic foundations

An analytical solution for buckling of an eccentrically stiffened sandwich truncated conical shell is investigated. The shell consists of two functionally graded material （FGM） coating layers and a core layer which are metal or ceramic subjected to an axial compressive load and an external uniform pressure. Shells are reinforced by stringers and rings, in which the material properties of shells and stiffeners are graded in the thickness direction following a general sigmoid law distribution. Two models of coated shell-stiffener arrangements are investigated. The change of the spacing between stringers in the meridional direction is taken into account. A couple set of three-variable- coefficient partial differential equations in terms of displacement components are solved by the Galerkin method. A closed-form expression for determining the buckling load is obtained. The numerical examples are presented and compared with previous works.

Finite element analysis of functionally graded sandwich plates with porosity via a new hyperbolic shear deformation theory

This study focusses on establishing the finite element model based on a new hyperbolic sheareformation theory to investigate the static bending,free vibration,and buckling of the functionally graded sandwich plates with porosity.The novel sandwich plate consists of one homogenous ceramic core and two different functionally graded face sheets which can be widely applied in many fields of engineering and defence technology.The discrete governing equations of motion are carried out via Hamilton’s principle and finite element method.The computation program is coded in MATLAB software and used to study the mechanical behavior of the functionally graded sandwich plate with porosity.The present finite element algorithm can be employed to study the plates with arbitrary shape and boundary conditions.The obtained results are compared with available results in the literature to confirm the reliability of the present algorithm.Also,a comprehensive investigation of the effects of several parameters on the bending,free vibration,and buckling response of functionally graded sandwich plates is presented.The numerical results shows that the distribution of porosity plays significant role on the mechanical behavior of the functionally graded sandwich plates。

Size-dependent effect on biaxial and shear nonlinear buckling analysis of nonlocal isotropic and orthotropic micro-plate based on surface stress and modified couple stress theories using differential quadrature method

The size-dependent effect on the biaxial and shear nonlinear buckling analysis of an isotropic and orthotropic micro-plate based on the surface stress, the modified couple stress theory （MCST）, and the nonlocal elasticity theories using the differential quadrature method （DQM） is presented. Main advantages of the MCST over the classical theory （CT） are the inclusion of the asymmetric couple stress tensor and the consideration of only one material length scale parameter. Based on the nonlinear von Karman assumption, the governing equations of equilibrium for the micro-classical plate consid- ering midplane displacements are derived based on the minimum principle of potential energy. Using the DQM, the biaxial and shear critical buckling loads of the micro-plate for various boundary conditions are obtained. Accuracy of the obtained results is validated by comparing the solutions with those reported in the literature. A parametric study is conducted to show the effects of the aspect ratio, the side-to-thickness ratio, Eringen＇s nonlocal parameter, the material length scale parameter, Young＇s modulus of the surface layer, the surface residual stress, the polymer matrix coefficients, and various boundary conditions on the dimensionless uniaxial, biaxial, and shear critical buckling loads. The results indicate that the critical buckling loads are strongly sensitive to Eringen＇s nonlocal parameter, the material length scale parameter, and the surface residual stress effects, while the effect of Young＇s modulus of the surface layer on the critical buckling load is negligible. Also, considering the size dependent effect causes the increase in the stiffness of the orthotropic micro-plate. The results show that the critical biaxial buckling load increases with an increase in G12/E2 and vice versa for E1/E2. It is shown that the nonlinear biaxial buckling ratio decreases as the aspect ratio increases and vice versa for the buckling amplitude. Because of the most lightweight micro-composite materials with high strength/weight and stiffness/weight ratios, it is anticipated that the results of the present work are useful in experimental characterization of the mechanical properties of micro-composite plates in the aircraft industry and other engineering applications.

Stress and buckling analysis of a thick-walled micro sandwich panel with a flexible foam core and carbon nanotube reinforced composite (CNTRC) face sheets

In this paper,the stresses and buckling behaviors of a thick-walled mi-cro sandwich panel with a flexible foam core and carbon nanotube reinforced composite(CNTRC)face sheets are considered based on the high-order shear deformation theory(HSDT)and the modified couple stress theory(MCST).The governing equations of equi-librium are obtained based on the total potential energy principle.The effects of various parameters such as the aspect ratio,elastic foundation,temperature changes,and volume fraction of the canbon nanotubes(CNTs)on the critical buckling loads,normal stress,shear stress,and deflection of the thick-walled micro cylindrical sandwich panel consider-ing different distributions of CNTs are examined.The results are compared and validated with other studies,and showing an excellent compatibility.CNTs have become very use-ful and common candidates in sandwich structures,and they have been extensively used in many applications including nanotechnology,aerospace,and micro-structures.This paper also extends further applications of reinforced sandwich panels by providing the modified equations and formulae.

Buckling analysis of super-long rock-socketed filling piles in soft soil area by element free Galerkin method

In order to discuss the buckling stability of super-long rock-socketed filling piles widely used in bridge engineering in soft soil area such as Dongting Lake, the second stability type was adopted instead of traditional first type, and a newly invented numerical analysis method, i.e. the element-free Galerkin method (EFGM), was introduced to consider the non-concordant deformation and nonlinearity of the pile-soil interface. Then, based on the nonlinear elastic-ideal plastic pile-soil interface model, a nonlinear iterative algorithm was given to analyze the pile-soil interaction, and a program for buckling analysis of piles by the EFGM (PBAP-EFGM) and arc length method was worked out as well. The application results in an engineering example show that, the shape of pile top load-settlement curve obtained by the program agrees well with the measured one, of which the difference may be caused mainly by those uncertain factors such as possible initial defects of pile shaft and the eccentric loading during the test process. However, the calculated critical load is very close with the measured ultimate load of the test pile, and the corresponding relative error is only 5.6%, far better than the calculated values by linear and nonlinear incremental buckling analysis (with a greater relative error of 37.0% and 15.4% respectively), which also verifies the rationality and feasibility of the present method.

Buckling Analysis of TF Coil Inner Leg for Central Solenoidless Tokamak

The central post is one of the critical components for the low aspect ratio tokamak, which endures not only a tremendous ohmic heating because it carries a rather high current, but also a large neutron heating and irradiation owing to the plasma operation. The DS copper alloy Glidcop AL-25[8] was chosen as the conductor material for its adequate mechanical properties and physics properties. The central post has a cylindrical structure with lots of cooling channels. The length of the central post for the next generation of nuclear fusion spherical tokamaks will be more than 10 m or 20 m. The structural stability is very crucial. When the applied load is larger than the structure critical buckling load, the device will lose its stability and collapse. In order to calculate the critical buckling load, a 1/6-segment finite element model was used and the force acting on the central post was simulated. The results showed that the vertical compressive stresses mainly affect the stability of the central post. The linear buckling analysis results with finite element method based on small deformation theory were given in this paper. The relation curves and functions for buckling factor, depending on the different lengths and the radius of the central post, the diameter of cooling channel and the maximum allowable current density, were also shown.

Linear Buckling Analysis of the HT-7U Vacuum Vessel

The vacuum vessel of the HT-7U superconducting Tokamak is designed as an allmetal welded double-wall structure with a number of radial and vertical ports. With characteristicsof ultrahigh vacuum and thin shell, the analysis on stability is very important to the design. Toachieve a successful final design, a threedimension buckling model has been performed using thefinite element program CoSMOS/M2.0. For all the cases having been considered, a 1/16 segmentof the whole toric shell are used to calculate the linear critical buckling load (Pc.,,) under auniform and nonwhform external pressure. As expected, the structure has a good capability ofwithstanding the applied loads.

Production TTR modeling and dynamic buckling analysis

In a typical tension leg platform (TLP) design,the top tension factor (TTF),measuring the top tension of a top tensioned riser (TTR) relative to its submerged weight in water,is one of the most important design parameters that has to be specified properly. While a very small TTF may lead to excessive vortex induced vibration (VIV),clashing issues and possible compression close to seafloor,an unnecessarily high TTF may translate into excessive riser cost and vessel payload,and even has impacts on the TLP sizing and design in general. In the process of a production TTR design,it is found that its outer casing can be subjected to compression in a worst-case scenario with some extreme metocean and hardware conditions. The present paper shows how finite element analysis (FEA) models using beam elements and two different software packages (Flexcom and ABAQUS) are constructed to simulate the TTR properly,and especially the pipe-in-pipe effects. An ABAQUS model with hybrid elements (beam elements globally + shell elements locally) can be used to investigate how the outer casing behaves under compression. It is shown for the specified TTR design,even with its outer casing being under some local compression in the worst-case scenario,dynamic buckling would not occur;therefore the TTR design is adequate.

VARIATIONAL PRINCIPLES OF PERFORATED THIN PLATES AND FINITE ELEMENT METHOD FOR BUCKLING AND POST-BUCKLING ANALYSIS

On the basis of the general theory of perforated thin plates under large deflections, variational principles with deflection w and stress function F as variables are stated in detail.Based on these princi- ples,finite element method is established for analysing the buckling and post-buckling of perforated thin plates. It is found that the property of element is very complicated,owing to the multiple connexity of the region.

Static and Buckling Analysis of Concrete Spherical Shells

A finite element analysis, including static and buckling analysis is presented for several notable concrete spherical shells around the world. Also, the structural optimization study of these shells was performed for thickness distribution and structure shape to reduce overall tensile stress, deflection and reinforcements. The finite element analysis using Sofistik software shows that a distributed concrete thickness reduces shell stresses, deflections and reinforcements. A geometrically non-linear analysis of these structures with and without imperfections was also performed. To take into account the possible plastification of the material an analysis with non-linear material was performed simultaneously with the geometrically non-linear analysis. This helps in developing an understanding of the structural behaviour and helps to identify all potential failure causes using failure analysis.

NONLINEAR BUCKLING ANALYSIS OF HYPERBOLIC COOLING TOWER SHELL WITH RING-STIFFENERS

This paper is concerned with a numerical solution of hyperbolic cooling tower shell, a class of full nonlinear problems in solid mechanics of considerable interest in engineering applications. In this analysis, the post-buckling analysis of cooling tower shell with discrete fixed support and under the action of wind loads and dead load is studied. The influences of ring-stiffener on instability load are also discussed. In addition, a new solution procedure for nonlinear problems which is the combination of load increment iteration with modified R-C are-length method is suggested. Finally, some conclusions having important significance for practice engineering are given.

ENDOCHRONIC ANALYSIS FOR COMPRESSIVE BUCKLING OF THIN－WALLED CYLINDERS IN YIELD REGION

The longitudinal compressive buckling of long and thin-walled cylinders in yield region is analyzed with the incremental and finite forms of the endochronic constitutive equation, respectively. The relations between the critical stress σ_(cr)versus the ratio of R (the radius) versus h (the thickness of the wall) are derived. The critical stress of the thin-walled cylinders made of abuminum alloys AMГ and 1T are analyzed and compared with the experimental data and the analytical results based on traditional theory of plasticity. It is seen that. except that the σ_(cr) of the cylinders made of 1Tpredicted by the finite form of the endochronic theory seems a little more conservative than that by traditional deformation theory of plasticity, in most cases, both forms of the endochornic constitutive equation provide more satisfactory results.

浮式海上风力发电机的时域响应结构分析

As the turbine blade size becomes larger for economic power production,the coupling effect between wind turbine and floating substructure becomes important in structural assessment.Due to unsteady turbulent wind environment and corresponding coupled substructure response,time-domain analysis is required by international electrotechnical commission and class societies.Even though there are a few numerical tools available for the time domain structural analysis based on conventional coupled motion analysis with wind turbine,the application of conventional time domain analysis is impractical and inefficient for structural engineers and hull designers to perform structural strength and fatigue assessment for the required large number of design load cases since it takes huge simulation time and computational resources.Present paper introduces an efficient time-domain structural analysis practically applicable to buckling and ultimate strength assessment.Present method is based on‘lodal’response analysis and pseudo-spectral stress synthesizing technique,which makes timedomain structural analysis efficient and practical enough to be performed even in personal computing system.Practical buckling assessment methodology is also introduced applicable to the time-domain structural analyses.For application of present method,a 15-MW floating offshore wind turbine platform designed for Korean offshore wind farm projects is applied.Based on full-blown time domain structural analysis for governing design load cases,buckling and ultimate strength assessments are performed for the extreme design environments,and the class rule provided by Korean Register is checked.

Local buckling of thin plate on tensionless elastic foundations under interactive uniaxial compression and shear

This paper uses a mathematical method to develop an analytical solution to the local buckling behaviour of long rectangular plates resting on tensionless elastic Winkler foundations and under combined uniform longitudinal uniaxial compressive and uniform in-plane shear loads. Fitted formulas are derived for plates with clamped edges and simplified supported edges. Two examples are given to demonstrate the application of the current method： one is a plate on tensionless spring foundations and the other is the contact between the steel sheet and elastic solid foundation. Finite element （FE） analysis is also conducted to validate the analytical results. Good agreement is obtained between the current method and FE analysis.

A Symplectic Method of Numerical Simulation on Local Buckling for Cylindrical Long Shells under Axial Pulse Loads

In this paper,the local buckling of cylindrical long shells is discussed under axial pulse loads in a Hamiltonian system.Using this system,critical loads and modes of buckling of shells are reduced to symplectic eigenvalues and eigensolutions respectively.By the symplectic method,the solution of the local buckling of shells can be employed to the expansion series of symplectic eigensolutions in this system.As a result,relationships between critical buckling loads and other factors,such as length of pulse load,thickness of shells and circumferential orders,have been achieved.At the same time,symmetric and unsymmetric buckling modes have been discuss.Moreover,numerical results show that modes of post-buckling of shells can be Bamboo node-type,bending type,concave type and so on.Research in this paper provides analytical supports for ultimate load prediction and buckling failure assessment of cylindrical long shells under local axial pulse loads.

Study on the Mechanical Properties of Irregular Curved Steel Box Girder for City Viaduct

This paper deeply analyses the influence of different local tectonic on stress performance of spatial curved steel box Girder Bridge, using the finite element analysis software to establish space finite element model of this bridge, calculation and analysis were made on the bridge of the strength, stiffness. It has certain reference value for guiding engineering design, have a good foundation for the mechanical properties and stability of linear and nonlinear further study of curved steel box girder.

Optimization and analysis of composite sandwich box beam for solar drones

Solar drones have garnered considerably research attention in recent years due to their continuous cruising capability,and the feasibility of design schemes is sensitive to the weight of structure.Sandwich box beam composed of carbon fiber and polymethacrylimide(PMI)foam is conducive to realize the lightweight of structure.In this study,a two-stage optimization design methodology for sandwich box beam is proposed.This methodology is primarily based on a low-order analytical method for evaluating stress/deflection and the linear buckling analysis method combined with experimental correction factor for predicting the buckling eigenvalues.Subsequently,a case study was conducted using an 18-m wingspan solar drone,where the results of mechanical test verified the optimization results.For validating the use of sandwich box beam in solar drones of other scales,additional analysis was conducted based on three aspects:(A)effects of stiffness and stability constraints on the design of sandwich box beam;(B)crucial role of the weight of foam inter layer and application scope of sandwich box beam;(C)best method to improve the buckling eigenvalue of sandwich box beam.Overall,the methodology and general rules presented in this paper can support the design of light wing beam for solar drones.