Symmetric Equations for Evaluating Maximum Torsion Stress of Rectangular Beams in Compliant Mechanisms

There are several design equations available for calculating the torsional compliance and the maximum torsion stress of a rectangular cross-section beam, but most depend on the relative magnitude of the two dimensions of the crosssection(i.e., the thickness and the width). After reviewing the available equations, two thickness-to-width ratio Independent equations that are symmetric with respect to the two dimensions are obtained for evaluating the maximum torsion stress of rectangular cross-section beams. Based on the resulting equations, outside lamina emergent torsional joints are analyzed and some useful design Insights are obtained. These equations, together with the previous work on symmetric equations for calculating torsional compliance, provide a convenient and effective way for designing and optimizing torsional beams in compliant mechanisms.

Numerical study on the thermo-stress of ZrO_2 thermal barrier coatings by high-intensity pulsed ion beam irradiation

This paper studies numerically the thermo-mechanical effects of ZrO2 thermal barrier coatings （TBCs） irradiated by a high-intensity pulsed ion beam in consideration of the surface structure. Taking the deposited energy of ion beams in TBCs as the source term in the thermal conduction equation, the distribution of temperature in TBCs was simulated. Then, based on the distribution, the evolution of thermal stress was calculated by the finite element method. The results show that tensile radial stress formed at the valley of TBC surfaces after irradiation by HIPIB. Therefore, if cracks happen, they must be at valleys instead of peaks. As for the stress waves, no matter whether through peak or valley position, tensile and compressive stresses are present alternately inside TBCs along the depth direction, and the strength of stress decreases with time.

Effects of zonal heat treatment on residual stresses and mechanical properties of electron beam welded TC4 alloy plates

Zonal heat treatment(ZHT) was conducted in situ to 14.5 mm-thick TC4 alloy plates by means of defocused electron beam after welding. The effects of ZHT on residual stresses,microstructures and mechanical properties of electron beam welded joints were investigated. Experimental results show residual stresses after welding are mostly relieved through ZHT,and the maximum values of longitudinal tensile stress and transverse compressive stress reduce by 76% and 65%,respectively. The tensile strength and ductility of welded joint after ZHT at slow scanning velocity are improved because of the reduction of residual stress and the microstructural changes of the base and weld metal. ZHT at fast scanning velocity is detrimental to the ductility of welded joint,which is resulted from insufficiently coarsened alpha phase in the fusion zone and the appearance of martensite in the base metal.

Fatigue Damage Modeling for Partially Prestressed Concrete Beams under Repeated Loadings with Variable Amplitude

A full-range nonlinear analysis method for fatigue damage in prestressed concrete beams is presented. New damage accumulation models are proposed to describe the fatigue damage evolution in concrete and reinforcement respectively. Based on the stress analysis for cross section, the stress redistrbution in the fatigue damage process, due to the different damage mechanisms of concrete and reinforcement, is considered. The nonlinear damage analysis is achieved by means of piecewise linearity, and it is applicable on the condition of repeated loadings with variable amplitude. Fatigue damage modeling of a beam is implemented to illustrate that the proposed method can preferably fit the experimental results.

Effect of ion-beam assisted deposition on the film stresses of TiO_2 and SiO_2 and stress control

Based on Hartmann-Shack sensor technique, an online thin film stress measuring system was introduced to measure the film stresses of TiO2 and SiO2, and comparison was made between the film stresses prepared respectively by the conventional process and the ion-beam assisted deposition. The effect of ion-beam assisted deposition on the film stresses of TiO2 and SiO2 was investigated in details, and the stress control methodologies using on-line adjustment and film doping were put forward. The results show that the film stress value of TiO2 prepared by ion-beam assisted deposition is 40 MPa lower than that prepared by conventional process, and the stress of TiO2 film changes gradually from tensile stress into compressive stress with increasing ion energy; while the film stress of SiO2 is a tensile stress under ion-beam assisted deposition because of the ion-beam sputtering effect, and the film refractive index decreases with increasing ion energy. A dynamic film stress control can be achieved through in-situ adjustment of the processing parameters based on the online film stress measuring technique, and the intrinsic stress of film can be effectively changed through film doping.

COMPUTATION OF SUPER-CONVERGENT NODAL STRESSES OF TIMOSHENKO BEAM ELEMENTS BY EEP METHOD

The newly proposed element energy projection(EEP) method has been applied to the computation of super_convergent nodal stresses of Timoshenko beam elements.General formulas based on element projection theorem were derived and illustrative numerical examples using two typical elements were given.Both the analysis and examples show that EEP method also works very well for the problems with vector function solutions.The EEP method gives super_convergent nodal stresses,which are well comparable to the nodal displacements in terms of both convergence rate and error magnitude.And in addition,it can overcome the “shear locking” difficulty for stresses even when the displacements are badly affected.This research paves the way for application of the EEP method to general one_dimensional systems of ordinary differential equations.

Residual stress analysis of 7075 aluminum alloy after vacuum electron beam welding

The residual stresses distribution of 7075 aluminum alloy in vacuum electron beam welding joint was numerically simulated using nonlinear finite element method. The result shows that the longitudinal residual stress is tension stress along weld center and the stress peak value appears in the middle of the welded seam; the transversal residual stress is compression stress ; the residual stress in thickness direction is very small.

TRANSVERSELY ISOIROPIC BEAM UNDER INITIAL STRESS

Starling from Novozhilov's nonlinear equations of elasticity by appropriate simplification and integration over the beam cross-section, a linearized set of equations for a transversely isotropic beam under initial non-uniform state of stress is obtained. In the absence of initial stress, the obtained equations are reduced to well-known Timoshenko beam equations.These equations are applied to investigate the vibration and buckling characteristics of a transversely isotropic beam under uniform initial axial force and bending moment.

FEM Simulation of Distortion and Residual Stress Generated by High Energy Beam Welding with Considering Phase Transformation

A series of experiments was carried out so as to elucidate the effect of the phase transformation in the cooling process on welding distortion and residual stress generated by laser beam welding (LBW) and laser-arc hybrid welding (HYBW) on the high strength steel (HT780). Then, the experiments were simulated by 3D thermal elasticplastic analysis with FEM (Finite Element Method) which was performed with using the idealized mechanical properties considering the transformation superplasticity. From the results, the effects of the phase transformation on welding distortion and residual stress generated by LBW and HYBW were elucidated. Furthermore, the generality of the idealization of the mechanical properties was verified.

Measurement of length-scale and solution of cantilever beam in couple stress elasto-plasticity

Owing to the absence of proper analytical solution of cantilever beams for couple stress/strain gradient elasto-plastic theory, experimental studies of the cantilever beam in the micro-scale are not suitable for the determination of material length-scale. Based on the couple stress elasto-plasticity, an analytical solution of thin cantilever beams is firstly presented, and the solution can be regarded as an extension of the elastic and rigid-plastic solutions of pure bending beam. A comparison with numerical results shows that the current analytical solution is reliable for the case of σ0 〈〈 H 〈〈 E, where σ0 is the initial yield strength, H is the hardening modulus and E is the elastic modulus. Fortunately, the above mentioned condition can be satisfied for many metal materials, and thus the solution can be used to determine the material length-scale of micro-structures in conjunction with the experiment of cantilever beams in the micro-scale.

Temperature stress analysis for bi-modulus beam placed on Winkler foundation

The materials with different moduli in tension and compression are called bi-modulus materials. Graphene is such a kind of materials with the highest strength and the thinnest thickness. In this paper, the mechanical response of the bi-modulus beam subjected to the temperature effect and placed on the Winkler foundation is studied. The differential equations about the neutral axis position and undetermined parameters of the normal strain of the bi-modulus foundation beam are established. Then, the analytical expressions of the normal stress, bending moment, and displacement of the foundation beam are derived. Simultaneously, a calculation procedure based on the finite element method （FEM） is developed to obtain the temperature stress of the bi-modulus struc- tures. It is shown that the obtained bi-modulus solutions can recover the classical modulus solution, and the results obtained by the analytical expressions, the present FEM proce- dure, and the traditional FEM software are consistent, which verifies the accuracy and reliability of the present analytical model and procedure. Finally, the difference between the bi-modulus results and the classical same modulus results is discussed, and several reasonable suggestions for calculating and optimizing the certain bi-modulus member in practical engineering are presented.

3D Finite Element Numerical Simulation of Residual Stresses on Electron Beam Welded BT20 Plates

A three-dimensional finite-element model (FEM) used for calculating electron beam (EB) welding temperature and stresses fields of thin plates of BT20 titanium has been developed in which the nonlinear thermophysical and thermo-mechanical properties of the material has been considered. The welding temperature field, the distributions of residual stresses in as-welded (AW) and electron beam local post-weld heat treatment (EBLPWHT) conditions have been successfully simulated. The results show that: (1) In the weld center, the maximum magnitude of residual tensile stresses of BT20 thin plates of Ti alloy is equal to 60%- 70% of its yield strength σs. (2) The residual tensile stresses in weld center can be even decreased after EBLPWHT and the longitudinal tensile stresses are decreased about 50% compared to joints in AW conditions. (3) The numerical calculating results of residual stresses by using FEM are basically in agreement with the experimental results. Combined with numerical calculating results, the effects of electron beam welding and EBLPWHT on the distribution of welding residual stresses in thin plates of BT20 have been analyzed in detail.

Effect of Overlap Stress as Well as Tie Beam Length and Width on Settlement of Isolated Footings Using Finite Element

Effects of tie beam length, width and overlap stress on settlement of foundations have been investigated. In this investigation square concrete footings have been used with dimensions (B × B × d) where (d) is footing depth and (B) is footing width (1, 1.5,2 m). Width of tie beam (b) has been taken equal to 0.25, 0.30, 0.40, 0.50 and 0.75 (m). Tie beam length (L) has been taken varying from B till 3B with same footing depth = 0.50 m. Effect of overlap stress on settlement as well as effect of tie beam width and length on settlement has been determined. Also, the efficiency of tie beam length and width has been obtained. An equation is presented to compute the overlap stress zone in case of existing tie beam. It is found that the settlement increases with increasing the length of tie beam which is clear after the effect of the overlap stresses zone. The width of overlap stress zone case of existing tie beam has been found to be equal to (1.6 -1.75) B. The settlement of footings decreases with increasing tie beam width. It is found that the settlement after the effect of the overlap stress zone increases with increasing the length of tie beam.

Finite element analysis on electron beam brazing temperature and stresses of stainless steel radiator

Based on thermal-elasto-plastic finite element theory, a two-dimensional finite element model for calculating electron beam brazing temperature and residual stress fields of stainless steel radiator are presented. The distributions of temperature and residual stress are studied. The resuhs showed that temperature distribution on brazing surface is rather uniform, ranging from 1 026 ℃ to 1 090 ℃. The residual stresses are varied from initial compressive to tensile , and the variation of residual stress is very little in total zone of brazing surface.

Fatigue tests of composite beam by steel fiber reinforced self-stressing concrete in the hogging bending

Through the experiments of 7 T-section composite beams, steel fiber reinforced self-stressing concrete （SFRSC） as the composite beam in the composite layer was studied under the hogging bending. The tests simulated composite layer tensile strain under the hogging bending of inverted loading composite beams, giving the relationship under the different fatigue stress ratios between fatigue cycles and steel bar’s stress range, crack width, stiffness loss and damage, etc., in composite layer. This article established fatigue life equation, and analyzed SFRSC reinforced mechanism to crack width and stiffness loss. The results show that SFRSC as the composite beam concrete has excellent properties of crack resistance and tensile, can reinforce the fatigue crack width and stiffness loss of composite beams, and improve the durability and in normal use of composite beams in the hogging bending zone.

NUMERICAL ANALYSIS OF RESIDUAL STRESSES IN TITANIUM ALLOY DURING ELECTRON BEAM LOCAL POST-WELD HEAT TREATMENT

The distributions of temperature and residual stresses in thin plates of BT20titanium alloy are numerically analyzed by three-dimensional finite element software duringelectron beam welding and electron beam local post-weld heat treatment (EBLPWHT). Combined withnumerical calculating results, the effects of different EBLPWHT mode and parameters, including heattreating position, heating width and heating time, on the distribution of welding residual stressesare analyzed. The results show that, the residual tensile stresses in weld center can be largelydecreased when the weld is heat treated at back preface of the plate. The numerical results alsoindicated that the magnitude of the residual longitudinal stresses of the weld and the zone vicinityof the weld is decreased, and the range of the residual longitudinal stresses is increased alongwith the increase of heating width and heating time.

系杆拱顶推施工方案及力学性能研究

为了探讨系杆拱结构的顶推方案及在顶推过程中的受力特点和设计要点,以某系杆拱桥的整体顶推施工工程为例,建立有限元模型,分析了系杆拱及导梁在不同顶推方案过程中的最值应力分布及挠度变形情况。研究结果表明:原吊杆连接方案(方案一)下,主梁及导梁变形过大,主梁应力过大,方案不可行,可通过增加梁高或者板厚来降低应力及变形,然而该法会造成外形不美观、造价偏高等情况;采用临时撑杆连接方案(方案二)时,受力得到优化,方案可行,然而靠近临时撑杆和端横梁的拱肋会出现较大应力,靠近顶推端部的两根临时撑杆中间主梁处会出现较大应力和变形;在导梁范围内,导梁端部会出现最不利挠度,需要注意控制导梁的整体刚度以及辅助墩上装置的竖向调节量,以免导梁和桥墩相撞。

预应力UHPC-NC组合梁结合面徐变剪应力分析

在恒载应力作用下,预应力UHPC-NC组合梁因两种材料不同的徐变特性及加载龄期的差异导致结合面产生徐变剪应力,分别采用解析法和有限元法对结合面徐变剪应力进行分析。在解析法中,用三角级数表示UHPC-NC结合面的应力分布,基于结合面上的变形协调,利用最小余能原理推导出结合面徐变剪应力计算公式。在有限元法中,将组合梁UHPC层与NC层均划分成四边形平面应力单元,对结合面则采用等效杆单元模拟。以T形截面预应力UHPC-NC组合梁为例进行计算方法的验证,两种方法的计算结果吻合良好,且研究发现徐变剪应力最大值位于梁端;在此基础上对影响结合面徐变剪应力分布的UHPC层压应力、梁高、计算龄期、环境年平均相对湿度等参数进行分析,结果表明:结合面徐变剪应力最大值随着UHPC层压应力、计算龄期、环境年平均相对湿度的增大而增大,但基本不随梁高变化;结合面徐变剪应力最大值的位置随着梁高的增大而逐步向跨中靠近,其他因素不影响应力最大值的位置。研究结果可为UHPC-NC组合梁结合面的抗剪设计提供参考。

Numerical stress analysis of crack at welded beam-to-column connection

In the past, brittle fracture of steel structure was reported rarely under earthquake. However, recent earthquakes, especially Northridge Earthquake (USA) and Hyogoken Nanbu earthquake (Japan), astonished engineers in the field of construction. The experience from recent earthquakes of USA and Japan shows that brittle fracture of welded steel structure always starts from high stress zone with welded crack [1～5] . As backing bar for grooved weld on beam flange exists, artificial crack is formed because of lack of fusion at the root of flange weld. In this paper stress distribution of connection is computed with FEM, and stress concentration at the root of flange weld is also analyzed. Stress intensity factors (SIFs), K I, at the root of flange weld are computed in the method of fracture mechanics. The computation shows that stress intensity factor on bottom flange weld is obviously higher than that on top flange weld. It is proved by the fact that brittle fracture is liable to start at the root of bottom flange weld on actual earthquake [1,4] . Finally measures are brought forward to avoid fracture of weld structure against earthquake.