GEOMETRICALLY NONLINEAR FINITE ELEMENT MODEL OF SPATIAL THIN-WALLED BEAMS WITH GENERAL OPEN CROSS SECTION

Based on the theory of Timoshenko and thin-walled beams, a new finite element model of spatial thin-walled beams with general open cross sections is presented in the paper, in which several factors are included such as lateral shear deformation, warp generated by nonuni- form torsion and second-order shear stress, coupling of flexure and torsion, and large displacement with small strain. With an additional internal node in the element, the element stiffness matrix is deduced by incremental virtual work in updated Lagrangian （UL） formulation. Numerical examples demonstrate that the presented model well describes the geometrically nonlinear property of spatial thin-walled beams.

Modeling and Free Vibration Behavior of Rotating Composite Thin-walled Closed-section Beams with SMA Fibers

Smart structure with active materials embedded in a rotating composite thin-walled beam is a class of typical structure which is using in study of vibration control of helicopter blades and wind turbine blades. The dynamic behavior investigation of these structures has significance in theory and practice. However, so far dynamic study on the above-mentioned structures is limited only the rotating composite beams with piezoelectric actuation. The free vibration of the rotating composite thin-walled beams with shape memory alloy（SMA） fiber actuation is studied. SMA fiber actuators are embedded into the walls of the composite beam. The equations of motion are derived based on Hamilton＇s principle and the asymptotically correct constitutive relation of single-cell cross-section accounting for SMA fiber actuation. The partial differential equations of motion are reduced to the ordinary differential equations of motion by using the Galerkin＇s method. The formulation for free vibration analysis includes anisotropy, pitch and precone angle, centrifugal force and SMA actuation effect. Numerical results of natural frequency are obtained for two configuration composite beams. It is shown that natural frequencies of the composite thin-walled beam decrease as SMA fiber volume and initial strain increase and the decrease in natural frequency becomes more significant as SMA fiber volume increases. The actuation performance of SMA fibers is found to be closely related to the rotational speeds and ply-angle. In addition, the effect of the pitch angle appears to be more significant for the lower-bending mode ones. Finally, in all cases, the precone angle appears to have marginal effect on free vibration frequencies. The developed model can be capable of describing natural vibration behaviors of rotating composite thin-walled beam with active SMA fiber actuation. The present work extends the previous analysis done for modeling passive rotating composite thin-walled beam.

Nonlinear Free Vibration Analysis of Thin-walled Curved Beam with Non-symmetric Open Cross Section

A finite element formulation was presented for the nonlinear free vibration of thin-walled curved beams with non-symmetric open across section. The kinetic and potential energies were derived by the virtual principle. The energy function includes the effect of fiexural-torsional coupling, the torsion warping and the shear centre location. For finite element analysis, cubic polynomials were utilized as the shape functions of the two nodal thin-walled curved elements. Each node possesses seven degrees freedom including the warping degree of freedom. The nonlinear eigenvalue problem was solved by the direct iteration technique. The results are compared with those for straight beams as available in the literature. The results for nonlinear free vibration analysis of curved beams for various radii and subtended angle are presented.

A new finite element of spatial thin-walled beams

Based on the theories of Timoshenko＇s beams and Vlasov＇s thin-walled members, a new spatial thin-walled beam element with an interior node is developed. By independently interpolating bending angles and warp, factors such as transverse shear deformation, torsional shear deformation and their Coupling, coupling of flexure and torsion, and second shear stress are considered. According to the generalized variational theory of Hellinger-Reissner, the element stiffness matrix is derived. Examples show that the developed model is accurate and can be applied in the finite element analysis of thinwalled structures.

A nonlinear explicit dynamic GBT formulation for modeling impact response of thin-walled steel members

A nonlinear explicit dynamic finite element formulation based on the generalized beam theory(GBT)is proposed and developed to simulate the dynamic responses of prismatic thin-walled steel members under transverse impulsive loads.Considering the rate strengthening and thermal softening effects on member impact behavior,a modified Cowper-Symonds model for constructional steels is utilized.The element displacement field is built upon the superposition of GBT cross-section deformation modes,so arbitrary deformations such as cross-section distortions,local buckling and warping shear can all be involved by the proposed model.The amplitude function of each cross-section deformation mode is approximated by the cubic non-uniform B-spline basis functions.The Kirchhoff s thin-plate assumption is utilized in the construction of the bending related displacements.The Green-Lagrange strain tensor and the second Piola-Kirchhoff(PK2)stress tensor are employed to measure deformations and stresses at any material point,where stresses are assumed to be in plane-stress state.In order to verify the effectiveness of the proposed GBT model,three numerical cases involving impulsive loading of the thin-walled parts are given.The GBT results are compared with those of the Ls-Dyna shell finite element.It is shown that the proposed model and the shell finite element analysis has equivalent accuracy in displacement and stress.Moreover,the proposed model is much more computationally efficient and structurally clearer than the shell finite elements.

Application of stiffness matrix of a beam element considering section distortion effect

According to the stationary principle of potential energy and the generalized coordinate method, a stiffness matrix of a beam element considering distortion effects is derived. Using the stiffness matrix of the beam element, a finite element program for computing thin-walled box steel beams is developed. And the program can take the section distortion and warping effects into account. The influences of diaphragm spacing on the mechanical behavior of thin-walled box beams are analyzed by the program. The numerical analysis shows that setting diaphragms have the greatest influence on the distortion normal stress, while there is very little influence on the bending normal stress. Only when the distance of adjacent diaphragms decreases to a certain value, will the distortion normal stress in the thin-walled box beam obviously reduce under the distortion load. Finally, a distortion-warping coefficient γ is introduced for simplifying the calculation of the longitudinal normal stress of thin-walled box beams. When the ratio of diaphragms adjacent space L to the maximum section dimension H is less than 2, the distortion-warping coefficient γ tends to one, which means that the distortion normal stress of the thin-walled box beam tends to zero, and the effect of the section distortion can be ignored.

Elastic buckling analysis and optimization of thin-walled bamboo-like pipe beam subjected to pure bending

In this paper,a stiffening design imitating the bamboo node is proposed for weight reduction of the long composite pipe beam subjected to bending load.The distribution of bamboo nodes can efficiently suppress the ovalization of the section,thus significantly improving the bending resistance of the bamboo.Based on this principle,ring stiffeners are proposed to be fixed to the pipe beam,making the long beam equivalent to the combination of a series of short pipes that suffered less section ovalization.A database of the optimal laminate orientations for different normalized lengths is obtained through optimizations,where the discreteness of the ply count is considered.Based on this database,weight optimizations are conducted,and the optimal designs of beams with and without stiffeners are obtained and compared.The comparison results show that the proposed bamboo-like stiffened beam not only regains a near-linear load–displacement relationship,but also reduces the weight by up to 16%under the same buckling load.In addition,it is found that for the pipe beams with radius-to-thickness ratios of more than 18,increasing the radius leads to a decrease in elastic buckling resistance when the weight remains a constant,which is opposite to the design for strength and stiffness.The model and database developed in this paper can provide a reference for weight reduction design and weight estimation for composite pipe beams.

Finite difference modeling of sinking stage curved beam based on revised Vlasov equations

For the static analysis of the sinking stage curved beam, a finite difference model was presented based on the proposed revised Vlasov equations. First, revised Vlasov equations for thin-walled curved beams with closed sections were deduced considering the shear strain on the mid-surface of the cross-section. Then, the finite difference formulation of revised Vlasov equations was implemented with the parabolic interpolation based on Taylor series. At last, the finite difference model was built by substituting geometry and boundary conditions of the sinking stage curved beam into the finite difference formulation. The validity of present work is confirmed by the published literature and ANSYS simulation results. It can be concluded that revised Vlasov equations are more accurate than the original one in the analysis of thin-walled beams with closed sections, and that present finite difference model is applicable in the evaluation of the sinking stage curved beam.

A new beam element for analyzing geometrical and physical nonlinearity

Based on Timoshenko＇s beam theory and Vlasov＇s thin-walled member theory, a new model of spatial thin-walled beam element is developed for analyzing geometrical and physical nonlinearity, which incorporates an interior node and independent interpolations of bending angles and warp and takes diversified factors into consideration, such as traverse shear deformation, torsional shear deformation and their coupling, coupling of flexure and torsion, and the second shear stress. The geometrical nonlinear strain is formulated in updated Lagarange （UL） and the corresponding stiffness matrix is derived. The perfectly plastic model is used to account for physical nonlinearity, and the yield rule of von Mises and incremental relationship of Prandtle-Reuss are adopted. Elastoplastic stiffness matrix is obtained by numerical integration based on the finite segment method, and a finite element program is compiled. Numerical examples manifest that the proposed model is accurate and feasible in the analysis of thin-walled structures.

Shear deformable finite beam elements for composite box beams

The shear deformable thin-walled composite beams with closed cross-sections have been developed for coupled flexural, torsional, and buckling analyses. A theoretical model applicable to the thin-walled laminated composite box beams is presented by taking into account all the structural couplings coming from the material anisotropy and the shear deformation effects. The current composite beam includes the transverse shear and the restrained warping induced shear deformation by using the first-order shear deformation beam theory. Seven governing equations are derived for the coupled axial-flexural-torsional-shearing buckling based on the principle of minimum total potential energy. Based on the present analytical model, three different types of finite composite beam elements, namely, linear, quadratic and cubic elements are developed to analyze the flexural, torsional, and buckling problems. In order to demonstrate the accuracy and superiority of the beam theory and the finite beam elements developed by this study,numerical solutions are presented and compared with the results obtained by other researchers and the detailed threedimensional analysis results using the shell elements of ABAQUS. Especially, the influences of the modulus ratio and the simplified assumptions in stress-strain relations on the deflection, twisting angle, and critical buckling loads of composite box beams are investigated.

Feasibility of developing composite action between concrete and cold-formed steel beam

Cold-formed steel structures are steel structure products constructed from sheets or coils using cold rolling, press brake or bending brake method. These structures are extensively employed in building construction industry due to their light mass, ductility by economic cold forming operations, favorable strength-to-mass ratio and other factors. The utilization of cold formed steel sections with concrete as composite can hugely reduce the construction cost. However, the use of cold formed steel members in composite concrete beams has been very limited. A comprehensive review of developments in composite beam with cold formed steel sections was introduced. It was revealed that employing cold-formed steel channel section to replace reinforcement bars in conventional reinforced concrete beam results in a significant cost reduction without reducing strength capacity. The use of composite beam consisting of cold-formed steel open or close box and filled concrete could also reduce construction cost. Lighter composite girder for bridges with cold-formed steel of U section was introduced. Moreover, types of shear connectors to provide composite action between cold-formed steel beam and concrete slab were presented. However, further studies to investigate the effects of metal decking on the behavior of composite beam with cold-formed steel section and introduction of ductile shear connectors were recommended.

龙门铣床横梁的工艺补偿研究

龙门铣床的横梁由于承载自身和主轴等关键零部件的质量,会产生严重变形,影响其几何精度,进而影响工件加工精度。因此,文章通过对横梁进行加工工艺补偿,来提高横梁的直线度。利用ANSYS Workbench对龙门铣床横梁进行静态特性研究,分析主轴在不同位置时横梁的最大变形区域和最大变形量,并以此为基础进行工艺补偿。借助激光干涉仪测量工艺补偿前后横梁的直线度,测量结果显示工艺补偿后横梁的直线度误差降低了90%,证实了工艺补偿对提高横梁几何精度的有效性与可行性。

Restrained torsion of open thin-walled beams including shear deformation effects

A first-order torsion theory based on Vlasov theory has been developed to investigate the restrained torsion of open thin-walled beams. The total rotation of the cross section is divided into a free warping rotation and a restrained shear rotation. In first-order torsion theory, St. Venant torque is only related to the free warping rotation and the expression of St. Venant torque is derived by using a semi-inverse method. The relationship between the warping torque and the restrained shear rotation is established by using an energy method. The torsion shear coefficient is then obtained. On the basis of the torsion equilibrium, the governing differential equation of the restrained torsion is derived and the corresponding initial method is given to solve the equation. The relationship between total rotation and flee warping rotation is obtained. A parameter λ, which is associated with the stiffness property of a cross section and the beam length, is introduced to determine the condition, under which the St. Venant constant is negligible. Consequently a simplified theory is derived. Numerical examples are illustrated to validate the current approach and the results of the current theory are compared with those of some other available methods. The results of comparison show that the current theory provides more accurate results, In the example of a channel-shaped cantilever beam, the applicability of the simplified theory is determined by the parameter study of λ.

A geometrical and physical nonlinear finite element model for spatial thin-walled beams with arbitrary section

Based on the theories of Bernoulli-Euler beams and Vlasov's thin-walled members,a new geometrical and physical nonlinear beam element model is developed by applying an interior node in the element and independent interpolations on bending angles and warp,in which factors such as traverse shear deformation,torsional shear deformation and their coupling,coupling of flexure and torsion,and second shear stress are all considered.Thereafter,geometrical nonlinear strain in total Lagarange(TL) and the corresponding stiffness matrix are formulated.Ideal plastic model is applied to physical nonlinearity to comply with the yield rule of Von Mises and incremental relationship of Prandtle-Reuss.Elastoplastic stiffness matrix is derived by numerical integration on the basis of the finite segment method.Examples show that the developed model is feasible in analysis of thin-walled structures with high accuracy.

不等间距拼宽T梁桥拼接段传力机理分析

为了验证广义梁格法计算的精确性,通过空间梁格法分析主梁非等间距拼宽对拼宽直梁桥受力性能的影响,并开展不同拼宽横梁间距对拼宽直梁桥内力横向分布的影响研究。结果表明:拼宽直梁桥广义梁格法计算内力横向分布的结果与空间梁格法计算所得的结果非常接近,各主梁挠度横向分布影响线计算结果最大偏差Δ_(dmax)在10%以内。主梁非等间距拼宽会使拼宽直梁桥的主梁内力横向分配变得不均匀,主梁拼宽间距(bc)<主梁一般间距(b0)时各主梁内力横向分布系数最大值与最小值的差值为0.533,比主梁等间距拼宽的差值大87.0%;bc>b0时各主梁内力横向分布系数最大值与最小值的差值为0.350,比主梁等间距拼宽的差值大23.2%。拼宽直梁桥的拼宽横梁受力性能分析可得:bc0时,拼宽横梁的弯矩影响线数值主要分布在负弯矩区;bc=b0时,拼宽横梁的弯矩影响线数值在正负弯矩区几乎均匀分布,bc>b0时,拼宽横梁的弯矩影响线数值主要分布在正弯矩区。因此在设计计算时,须考虑正弯矩和负弯矩的绝对值的最大值进行设计。

Vibration and flutter of wind turbine blade modeled as anisotropic thin-walled closed-section beam

Based on a variational asymptotic analytical model, vibration and aeroelastic stability of rotor blades modeled as anisotropic thin-walled closed-section beams are systematically addressed. The analysis is applied to a laminated composite construction of the circumferentially asymmetric stiffness (CAS) that produces bending-twist coupling. The vibration characteristics of composite beam are determined by the Extended Galerkin Method. The unsteady aerodynamic loads and centrifugal force are integrated with the classical aerodynamic model to deal with aeroelastic stability analysis. The influence of some related factors, ply angle, rotating velocity, and wind speed, is investigated. The paper gives methods of eigenvalue analysis and aeroelastic response, and gives the approaches to restrain classical flutter.

深中通道中山大桥超宽钢箱梁悬臂拼装横向变形分析及对策措施

针对斜拉桥超宽幅钢箱悬臂拼装过程中存在横向变形问题,该文根据深中通道中山大桥双向八车道超宽钢箱梁施工特点,分析超宽钢箱梁悬拼安装过程中横向变形产生的主要原因,结合目前国内外宽幅箱梁悬拼施工中匹配高差调整工艺,创新性地提出“一字梁锁定+挂索初张拉匹配”工艺,较好地解决了中山大桥超宽钢箱梁悬臂拼装横向变形差问题。

曲杆结构非线性分析中的直梁单元和曲梁单元

采用直梁单元 ,编制了杆系结构的几何非线性有限元程序。通过 2个曲杆结构的实例 ,对采用直梁单元和多种曲梁单元的有限元计算进行了对比。结果表明 ,采用两类单元的计算结果没有明显的差别。因而 ,在杆系结构的非线性分析中 ,可以采用直梁单元来模拟曲梁 ,进行屈曲分析。

基于共路光线漂移补偿的直线度测量

针对影响激光测量直线度误差的主要因素之一激光光线漂移,提出了一种基于共路光线漂移补偿的直线度误差测量方法,给出了具体的测量原理和系统构成。从产生激光光线漂移的几个因素出发,理论分析了所产生的光线漂移对直线度误差测量的影响,建立了相对应的光线漂移补偿模型。结果表明,进行补偿后激光器出射光线引起的光线漂移在X方向的最大漂移量由28.4μm减少为5.6μm,Y方向的最大漂移量由21.6μm减少到5μm;由温度梯度引起的光线漂移经补偿后最大漂移量由65.7μm减少为8.9μm。实验结果与理论分析均表明,该方法能有效减少各种因素引起的光线漂移对直线度测量结果的影响,提高测量直线度误差的准确性。

日光直射下混凝土梁的力学响应

依据热量平衡原理建立混凝土梁结构在等强度日光直射下的瞬态热传导数学模型,依据此模型导出其内部温度场的解析解,由此得到日光直射下混凝土梁在任意时刻的温度分布.通过弹性理论由位移法求解得出梁在该温度场下的温度应力及热变形响应,分析了温度应力随日光照射时间的变化;为验证数学模型的有效性,进行了日光照射模拟实验,采用碳纤维混凝土涂层梁的电热效应使梁内温度场发生变化,并将梁上下表面的温差及梁跨中挠度与模拟实验结果进行了比较;分析了混凝土材料的导热系数对温度应力和变形的影响,由此结果说明可以通过提高混凝土材料的导热系数来减小日照引起的温度应力及变形.