Influence of Multiple Micro Cracks on the Damage Behavior of a Macro-Crack Tip北大核心CSCD

The solution of an infinite plane containing a macro crack and a cluster of micro cracks under uniaxial tensile load was presented based on Muskhelishvili’s complex function method and the stepwise recursive method. The stress field and stress intensity factor K were obtained. Combined with the damage mechanics, damage parameter D of the macro-crack tip and the micro-crack tip under uniaxial tension was redefined, and the influence of different damage zone forms on the damage of the crack tip was analyzed. The results show that, both the chain-distribution and the reverse-chain-distribution micro cracks have an amplifying effect on the macro crack growth, and the damage parameter increases with the decrease of the inclination angle of the micro crack and the reduction of the distance between the macro crack and the micro cracks. For a relatively small inclination angle of the micro crack, the damage parameters of the macro crack and the micro crack heightens, and the damage parameter of the macro crack increases with the micro-crack length. For evenly distributed micro cracks in the continuous damage zone, the micro cracks have an amplifying effect on the macro-crack growth, and the damage parameter of the macro crack increases with the micro-crack number. © 2022 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

Experimental Study on the Flexural Ductility of BFRP Bar Concrete Beams With Bamboo Fiber and Steel Wire Mesh北大核心CSCD

To study the effects of bamboo fiber and steel wire mesh on the flexural ductility of basalt fiber reinforced polymer（BFRP）bar concrete beams, 7 BFRP bar concrete beams with bamboo fiber and steel wire mesh were tested with different bamboo fiber lengths (0 mm, 30 mm and 45 mm) and different steel wire mesh layout ranges (0, 1/2 maximum bending moment point layout and full beam length layout). The flexural failure tests of the 7 beams were carried out, and the initial crack loads, the crack developments, the ultimate loads and the deformations were detected. The effects of the fiber length and the wire mesh layout range on the crack resistance and the deformation resistance of the specimens were analyzed based on the test data. With the function model, the equivalent yield points of the 7 test beams were obtained, and their ductility coefficients were calculated. The results show that, the addition of bamboo fiber and steel wire mesh increases the cracking loads of BFRP bar concrete beams by 12%~68%, decreases the crack spacings and the crack length development speed, reduces the test beam deformation under the same load, and increases the ductility coefficient by 1.58%~31.75%. © 2023 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

Existence of Positive Solutions for Eigenvalue Problems of Fourth-order Elastic Beam Equations

In this paper,we investigate the positive solutions of fourth-order elastic beam equations with both end-points simply supported.By using the approximation theorem of completely continuous operators and the global bifurcation techniques,we obtain the existence of positive solutions of elastic beam equations under some conditions concerning the first eigenvalues corresponding to the relevant linear operators,when the nonlinear term is non-singular or singular,and allowed to change sign.     

Dynamic response of planar interface crack between viscoelastic bodies

IntroductionThe dynamic stress intensity factor (SIF) plays an important role in dynamic fracture underboth harmonic and transient loads. It predicts whether or not the fracture toughness of thematerial will be exceeded and catastrophic crack propagation will follow. The dynamic SIFof interfaCe cracks between two dissimilar elastic materials has been studied widely. Kundull]studied the dynamic SIF of interface crack under transient loading with the method based onBetti's reciprocal theore…     

Secondary Buckling Analysis of Thin Rectangular Plates Based on the Wavelet Galerkin Method北大核心CSCD

Application of the wavelet Galerkin method (WGM) to numerical solution of nonlinear buckling problems was studied with classical elastic thin rectangular plates. First, the discretized scheme of the von Kármán equation were introduced, then a simple calculation approach to the Jacobian and Hessian matrices based on the WGM was proposed, and the wavelet discretized scheme-based eigenvalue equation method, the extended equation method and the pseudo arc-length method for nonlinear buckling analysis were discussed. Second, the secondary post-buckling equilibrium paths of elastic thin rectangular plates and the effects of aspect ratios, boundary conditions and bi-directional compression on the mode jumping behaviors, were discussed in detail. Numerical results show that, the WGM possesses good convergence for solving buckling loads on rectangular plates, and the obtained equilibrium paths are in good agreement with those from the stability experiments, the 2-step perturbation method and the nonlinear finite element method. Given the feasibility of combination with different bifurcation computation methods, the WGM makes an efficient spatial discretization method for complex nonlinear stability problems of typical plates and shells. © 2023 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

Numerical Approximation and Error Analysis for the Timoshenko Beam Equations with Boundary Feedback

In this paper,the numerical approximation of a Timoshenko beam with bound- ary feedback is considered.We derived a linearized three-level difference scheme on uniform meshes by the method of reduction of order for a Timoshenko beam with boundary feedback.It is proved that the scheme is uniquely solvable,unconditionally stable and second order convergent in L_∞norm by using the discrete energy method. A numerical example is presented to verify the theoretical results.     

Stress intensity factors for a finite plate with an inclined crack by boundary collocation

In this paper, we combine the Muskhelishvili＇s complex variable method and boundary collocation method, and choose a set of new stress function based on the stress boundary condition of crack surface, the higher precision and less computation are reached. This method is applied to calculating the stress intensity factor for a finite plate with an inclined crack. The influence of θ （the obliquity of crack） on the stress intensity factors, as well as the number of summation terms on the stress intensity factor are studied and graphically represented.     

COPLANAR CRACKS IN A FINITE TRANSVERSELY ISOTROPIC ELASTIC SLAB UNDER ANTIPLANE SHEARL STRESSES

An antiplane crack problem concerning a pair of coplanar cracks in a finite transversely isotropic elastic slab is considered. Using Fourier integral transform together with singular integral equation which can be solvel numerically by suing a collocation technique. Once the integral equation is solved, the relevant crack energy and stress intensity factors of the problem are given. The analysis present can be easily extended to include cases where there are two or more pairs of coplanar cracks in the slab.     

Identification of Pipeline Inner Wall Geometry Based on the POD⁃RBF Method北大核心CSCD

Based on the proper orthogonal decomposition⁃radial basis function (POD⁃RBF), a geometric identification method for pipeline inner wall was proposed to solve the internal corrosion detection problem of natural gas and oil pipelines. In view of the static magnetic field, the simplified finite element model for the pipelines was established, and the variable⁃geometry sample library was constructed, to realize the response prediction of arbitrary geometry by the POD⁃RBF. The proposed method achieves reduced⁃order analysis and avoids repeated solution of the stiffness matrix due to the geometrical change during the identification process. Hence, it can significantly improve the computation efficiency. Finally, the grey wolf optimization (GWO) algorithm was used to optimize the objective function and avoid the calculation of the sensitivity in the process of geometry change. The numerical examples show that, the proposed method has high efficiency and accuracy in the geometric identification of the pipeline inner wall, with good stability even under introduced noises. © 2023 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

Effects of Cone Angles on Nonlinear Vibration Responses of Functionally Graded Shells北大核心CSCD

The nonlinear vibration responses of functionally graded materials (FGMs) shells with different cone angles under external loads were studied. Firstly, the Voigt model was employed to describe the physical properties along the thickness direction of FGMs conical shells. Then, the motion equations were derived based on the 1st-order shear deformation theory, the von Kármán geometric nonlinearity and Hamilton’s principle. Next, the Galerkin method was applied to discretize the motion equations and the governing equations were simplified into a 1DOF nonlinear vibration differential equation under Volmir’s assumption. Finally, the nonlinear motion equations were solved with the harmonic balance method and the Runge-Kutta method, and the amplitude frequency response characteristic curves of the FGMs conical shells were obtained. The effects of different material distribution functions and different ceramic volume fraction exponents on the amplitude frequency response curves of conical shells were discussed. The bifurcation diagrams of conical shells with different cone angles, as well as time process diagrams and phase diagrams for different excitation amplitudes, were described. The motion characteristics were characterized by Poincaré maps. The results show that, the FGMs conical shells present the nonlinear characteristics of hardening springs. The chaotic motions of the FGMs conical shells are restrained and not prone to motion instability with the increase of the cone angle. The FGMs conical shell present a process from the periodic motion to the multi-periodic motion and then to chaos with the increase of the excitation amplitude. © 2022 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

双层0.618法在某力学问题中的应用

建立了一组平行移动荷载作用下,简支桥梁挠度的数学模型;利用双层0.618法搜索梁的绝对最大挠度对应的最危险截面位置以及移动荷载最不利位置,计算该位置相应的挠度得到梁的绝对最大挠度.本文算法以计算机为工具,适用于任意有限多个平行移动荷载,对于桥梁的设计计算与安全评估,有一定的实用价值.     

空间一维结构分布动载荷时域识别方法

提出一种适用于空间一维结构分布动载荷的时域识别方法.基于空间分段和时间分段的思想, 推导了载荷时程识别的公式和过程.用MATLAB编写了载荷识别程序,以受分布动载荷简支梁和受随机风载荷输电导线的载荷识别对方法和程序进行验证, 并通过仿真试验研究了噪声对载荷识别的影响.结果表明,该方法对于线性问题有很高的识别精度,对于弱非线性问题能够满足工程应用要求,为分布动载荷时域识别提供了有效的途径.     

Crack identification of the sprocket wheel in sintering machine based on WFEM

In order to identify the crack of the sprocket wheel correctly, the wavelet finite element method is studied in depth. Firstly, the progress of study on the wavelet finite element method is summarized, and then the basic property of wavelet analysis is analyzed, and then the wavelet finite element theory model of sprocket wheel in sintering machine is studied, and the Daubechies wavelet plate element and isoparametric plate element of crack tip are established, and then the theory of constructing crack identification database of the crack for sprocket wheel is studied, and finally the effective of this method is verified by identify the sprocket wheels with five kinds of cracks based on the vibration test, and results showed that this method can identify the crack of the sprocket wheel correctly.     

黄金分割算法在简支桥梁设计计算中的应用

移动荷载作用下,简支桥梁横截面上弯矩的变化为二元函数Z=f(x,y),本文给出了绝对最大弯矩Zm ax的极值点x*、y*的判别方法:利用数学中的黄金分割算法搜索梁的绝对最大弯矩对应的最危险横截面位置x*;利用力学中的影响线理论判别该截面发生最大弯矩时的最危险荷载位置y*,计算该横截面的最大弯矩得到梁的绝对最大弯矩.该算法易于编写计算程序,以计算机为工具,适用于任意有限多个平行移动荷载在桥梁上移动,对于桥梁的设计计算与安全评估,有一定的实用价值.     

Nonlinear breathing crack identification from time-domain sensitivity analysis

Breathing cracks are often encountered in engineering structures and detection of such cracks at the earliest stage is important for safety and serviceability of the structures. In this paper, a new breathing crack identification approach based on the time-domain sensitivity analysis is proposed. For the forward problem, the crack is simply treated as a nonlinear oscillator and how to model a structure with breathing cracks is specified. As regards the inverse crack identification, it is formulated as a nonlinear least-squares optimization problem and a new sensitivity-based approach is developed to get the solution. In doing so, the sensitivity analysis of the possibly non-differentiable breathing crack models is necessarily proceeded through a smoothing strategy. Moreover, to enhance the convergence, the trust-region constraint is introduced and the Tikhonov regularization is naturally called to tackle the constraint. Numerical examples are studied to verify the feasibility and efficiency of the proposed approach in breathing crack identification.     

Critical state of a thin-walled beam under combined load

Subject of the paper is a simply supported thin-walled beam. The beam carries uniformly distributed transverse load, small axial force and two different moments located at its both ends. The elastic potential energy and the work of the loads for the beam are described. Basing on the minimum of the total potential energy the general algebraic equation of the critical state for the beam is obtained. The equation describes a convex hyper-surface. Particularly simply load cases are studied. Based on the general equation of the critical state numerical investigations are realized. The results are shown in figures.     

变刚度复杂梁结构损伤检测方法研究

提出了适用于复杂梁结构损伤检测的子段模态应变能法SSEM(subsectionstrainenergymethod),并分析了该方法的适用性条件．通过对变截面梁的有限元计算,以及对纤维增强复合材料风机叶片缩比模型的试验分析,验证了SSEM方法确定的结构损伤指标对损伤准确定位的可靠性．该基于振动的变刚度复杂梁结构的损伤检测方法,可应用于工程实际中梁和类梁整体结构的损伤检测．     

四点弯曲压电梁导电裂纹尖端附近的横观各向同性损伤

根据电焓密度函数建立了压电材料静态损伤本构模型,详细讨论了横观各向同性力电损伤的一些特征,最后通过对四点弯曲PZT-PIC151梁跨中导电裂纹附近横观各向同性损伤的数值分析,研究了裂纹深度和外加力、电载荷对损伤分布的影响规律．结果表明:裂纹深度和力载荷对力电损伤都有非常明显相似的影响,随着裂纹深度和力载荷的增大,裂纹尖端的力电损伤明显增大,范围也相应扩大;电载荷对力损伤完全不同于对电损伤的影响,电载荷单调地改变裂纹尖端力损伤的大小,不改变力损伤的区域尺寸,但是对电损伤的影响则比较复杂．     

Analytical study on dynamic responses of a curved beam subjected to three-directional moving loads

Considering the warping resistance, inertia force and moving three-directional loads, a more comprehensive set of governing equations for vertical, torsional, radial and axial motions of the curved beam are derived. The analytical solutions for vertical, torsional, radial and axial responses of the curved beam subjected to three-directional moving loads are obtained, using the Galerkin method to discretize the partial differential equations and the modal superposition method to decouple the ordinary differential equations. The analytical results are compared with the numerical integration and a published work to verify the validity of the proposed solutions. Effects of Galerkin truncation terms and damping ratio on solution convergence are also discussed. Considering first-mode and higher-mode truncation respectively, the conditions of resonance and cancellation are analyzed for vertical, torsional, radial and axial motions of the curved beam. Taking a curved bridge under passage of a vehicle as an example, the influences of system parameters, such as vehicle speed, braking acceleration, bridge curve radius, bridge span and bridge deck elastic modulus, on bridge midpoint vibration are explored. The proposed approach and results may be beneficial to enhance understanding the three-directional vehicle-induced dynamic responses of curved bridges. It is shown that when the axial motion, or the multiple moving loads are involved, the first-order truncation are not accurate enough and one should use higher-mode truncation to study the responses of curved beams. In addition, it is necessary to consider damping in the vibration study of curved beams.     

Influence of Initial Stresses on Stress Intensity Factors at Crack Tips in a Composite Strip

The influence of initial tension or compression along cracks on the stress intensity factor (SIF) at crack tips under the action of additional normal forces on crack edges is studied for infinite bodies. A strip made of a composite material is considered. The strip ends are simply supported, and the strip contains a crack whose edges are parallel to its face planes. The strip is first stretched or compressed along crack edges, and then additional uniformly distributed normal forces are applied to the crack edges. The influence of the initial tension (compression) on the SIF caused by the additional normal forces is studied. The corresponding boundary-value problems are modelled with the use of the three-dimensional linearized theory of elasticity. All the investigations are carried out numerically by employing the finite-element method. The values of SIF are calculated by the energy release method.