Enhancing Stress Intensity Factor Reduction in Cracks Originating from a Circular Hole in a Rectangular Plate under Uniaxial Stress through Piezoelectric Actuation

Circular holes are commonly employed in engineering designs;however, they often serve as locations where cracks initiate and propagate. This paper explores a novel approach to structural repair by utilizing piezoelectric actuators. The primary focus of this study is to investigate the influence of an adhesively bonded piezoelectric actuator patch placed above a circular hole on the stress intensity factor (SIF) in an aluminium plate. The plate is subjected to uniaxial tensile stress, while the piezoelectric actuator is excited with varying voltage levels. The analysis is conducted using the finite element method (FEM), a powerful numerical technique for simulating complex structures. The study assesses the stress distribution and employs the SIF as an adequate criterion for evaluating the impact of different patch configurations. The results indicate a strong correlation between the applied voltage and the SIF. Whether the SIF increases or decreases depends on the polarization of the piezoelectric actuator. Particularly noteworthy is the finding that rectangular patches in a horizontal orientation significantly reduce the SIF compared to other patch geometries. Moreover, double-sided patches exhibit a pronounced decrease in the SIF compared to single-sided patches. In summary, this research underscores the potential of piezoelectric actuators in mitigating stress intensity in structures with circular hole with crack initiation. It offers valuable insights into the influence of applied voltage, patch geometry, and patch placement on the SIF, thereby contributing to developing effective strategies for enhancing structural integrity.

Least Square Finite Element Model for Analysis of Multilayered Composite Plates under Arbitrary Boundary Conditions

Laminated composites are widely used in many engineering industries such as aircraft, spacecraft, boat hulls, racing car bodies, and storage tanks. We analyze the 3D deformations of a multilayered, linear elastic, anisotropic rectangular plate subjected to arbitrary boundary conditions on one edge and simply supported on other edge. The rectangular laminate consists of anisotropic and homogeneous laminae of arbitrary thicknesses. This study presents the elastic analysis of laminated composite plates subjected to sinusoidal mechanical loading under arbitrary boundary conditions. Least square finite element solutions for displacements and stresses are investigated using a mathematical model, called a state-space model, which allows us to simultaneously solve for these field variables in the composite structure’s domain and ensure that continuity conditions are satisfied at layer interfaces. The governing equations are derived from this model using a numerical technique called the least-squares finite element method (LSFEM). These LSFEMs seek to minimize the squares of the governing equations and the associated side conditions residuals over the computational domain. The model is comprised of layerwise variables such as displacements, out-of-plane stresses, and in- plane strains, treated as independent variables. Numerical results are presented to demonstrate the response of the laminated composite plates under various arbitrary boundary conditions using LSFEM and compared with the 3D elasticity solution available in the literature.

Prediction model of residual stress field in aluminum alloy plate

Residual stress distributions in 7075 aluminum alloy thick plates with different thicknesses and different quenching speeds were measured. A shape function of stress distribution was proposed based on the internal stress distribution characteristics of aluminum alloy. Using nonlinear regression technology,the function between stress value of key points on internal stress curve and surface stress of the plate was obtained. Based on the measured surface stress,stress value of key points and stress distribution shape,the internal stress distribution can be reconstructed. The experiments show that the model is of good engineering practicality.

MODIFIED LAYER REMOVAL METHOD FOR MEASUREMENT OF RESIDUAL STRESS DISTRIBUTION IN THICK PRE-STRETCHED ALUMINUM PLATE

The integrated structure parts are widely used in aircraft. The distortion caused by residual stresses in thick pre-stretched aluminum plates during machining integrated parts is a common and serious problem. To predict and control the machining distortion, the residual stress distribution in the thick plate must be measured firstly. The modified removal method for measuring residual stress in thick pre-stretched aluminum plates is proposed and the stress-strain relation matrix is deduced by elasticity theory. The residual stress distribution in specimen of 7050T7451 plate is measured by using the method, and measurement results are analyzed and compared with data obtained by other methods. The method is effective to measure the residual stress.

Numerical simulation about the effect of fixture on the welding stress and distortion of thin aluminum plate joints

The effect of welding jig on the welding stress and buckling distortion of thin aluminum plate joints was simulated by finite element method （FEM）. The results show that the restraint distance and the heat conduction ability of the fixture do have essential effects on the residual stress and distortion. The residual compressive stress and distortion will be increasing with the increase of the restraint distance, while the residual compressive stress and distortion will be decreasing with the increase of the heat conduction ability of the fixture.

Residual stress in quenched 7075 aluminum alloy thick plates

The influence of quenching water temperature, pre stretching amount and aging temperature and times on residual stress in 7075 aluminum thick plate was studied by the measurement of residual stress using drilling hole method. The results indicate that residual stress decreases by 30% with increasing quenching water temperature from 40 ℃ to 80 ℃, 20% with increasing aging temperature from 100 ℃ to 180 ℃,and 20% with increasing aging times from 5 h to 25 h. Also, residual stress decreases to zero with increasing pre stretching amount to approximately 2%. Hence, residual stress in 7075 aluminum thick plate is reduced by the control of quenching water temperature at 80 ℃ and with pre stretching amount of about 2%. An optimal aging temperature and time should be systemically investigated to obtain combination of high mechanical performances and lower residual stress for manufacturing of 7075 aluminum alloy thick plates.

Regional characteristics of stress field in the southern part of the north－south seismic belt in China and its relation with plate movement

The regional characteristics of stress field in the southern part of the northusouth seismic belt (NSB) have beenanalyzed in detail based on the mechanism solutions of 134 medium and large earthquakes from 1933 to 1991.The results show that the southern part of the NSB is a shallow earthquake zone where most earthquakes arecaused by the strike-slip faulting. There is a systematic distribution of the directions of P-and T-axes in thewestern and the eastern regions of the southern part of the NSB. P-and T-axes in the western region are in theNE-SW direction and in the NW-SE direction. P-and T-axes in the eastern region are oriented in NW-SE andNE-SW, respectively. The directions of p-axes in the western and the eastern regions show a pattern of a reversal 'V' as a whole. The boundary between the eastern and western regions coincides with that between the Tibetan Plateau and the Yangtze crustal block. Based on a lot of mechanism solutions, the result indicates that thedirection of P-axes roughly shows the consistent distributions from the Himalayan collision zone to the easternregion and from the eastern coast collision zone in Taiwan to the eastern region of southern part of the NSB, respectively. It is suggested that the tectonic force due to relative movement between the indo-Australian and theEurasian plates is transmitted from the Himalayan collision zone to the western region of the southern part ofNSB, simultaneously, the tectonic force due to the relative movement between the Philippine Sea and theEurasian plates is transmitted from the eastern region coast in Taiwan to the eastern region of the southern partof NSB, and control the stress field there, respectively.

Modified Layer-Removal Method for Measurement of Residual Stress in Pre-stretched Aluminium Alloy Plate

Residual stress is one of the factors affecting the machining deformation of monolithic structure parts in the aviation industry. Thus,the studies on machining deformation rules induced by residual stresses largely depend on correctly and efficiently measuring the residual stresses of workpieces. A modified layer-removal method is proposed to measure residual stress by analysing the characteristics of a traditional layer-removal method. The coefficients of strain release are then deduced according to the simulation results using the finite element method( FEM). Moreover,the residual stress in a 7075T651 aluminium alloy plate is measured using the proposed method,and the results are then analyzed and compared with the data obtained by the traditional methods. The analysis indicates that the modified layer-removal method is effective and practical for measuring the residual stress distribution in pre-stretched aluminium alloy plates.

DYNAMIC STRESS CONCENTRATIONS IN AMBARTSUMIAN'S PLATE WITH A CUTOUT

Based on the motion equations of flexural wave in Ambartsumian' s plates including the effects of transverse shear deformations,by using perturbation method of small parameter,the scatter- ing of flexural waves and dynamic stress concentrations in the plate with a cutout have been studied. The asypmtotic solution of the dynamic stress problem is obtained.Numerical results for the dynamic stress concentration factor in Ambartsumian's plates with a circular cutout are graphically presented and discussed.

ANALYTICAL VARIATIONAL METHOD OF SOLUTION FOR STRESS CONCENTRATION FACTORS OF FINITE PLATES WITH A PIN HOLE

First of all, Laurent series expansions of stress and displacement fields satisfying all the governing equations of plane problems in theory of elasticity are derived. Next, the variational method is applied to satisfy the boundary conditions of a plate with a pin hole. Then, the coefficients in Laurent series and the stress concentration factor can be determined. Finally, the convergency tests and systematical results are given for engineering applications.

THE EVALUATION OF STRESS INTENSITY FACTORS OF PLANE CRACK FOR ORTHOTROPIC PLATE WITH EQUAL PARAMETER BY F2LFEM

In this paper, the evaluation of stress intensity factor of plane crack problems for orthotropic plate of equal-parameter is investigated using a fractal two-level finite element method （F2LFEM）. The general solution of an orthotropic crack problem is obtained by assimilating the problem with isotropic crack problem, and is employed as the global interpolation function in F2LFEM. In the neighborhood of crack tip of the crack plate, the fractal geometry concept is introduced to achieve the similar meshes having similarity ratio less than one and generate an infinitesimal mesh so that the relationship between the stiffness matrices of two adjacent layers is equal. A large number of degrees of freedom around the crack tip are transformed to a small set of generalized coordinates. Numerical examples show that this method is efficient and accurate in evaluating the stress intensity factor （SIF）.

CALCULATION OF STRESSES IN A MULTIPLY-CONNECTED ANISOTROPIC PLATE USING STRESS FUNCTIONS OF MULTIPLE COMPLEX VARIABLES

On the basis of anisotropic mathematical elasticity,using multiple conformal representations, the stress functions of multiple complex variables for an infinite multiply-connected anisotropic plate are de- rived.The functions are developed in Fourier series on unit circles,and the unknown coefficients of the functions are determined by undetermined coefficients method.Then the stresses in the plate can be calcu- lated.A plate containing multiple elliptical holes or cracks is discussed,and the corresponding FORTRAN77 program is developed.Five examples are given.The results show that this method is very effective and convenient.

SCATTERING OF FLEXURAL WAVES AND DYNAMIC STRESS CONCENTRATIONS IN MINDLIN'S THICK PLATES WITH A CUTOUT

Using the complex variable method and conformal mapping,scat- tering of flexural waves and dynamic stress concentrations in Mindlin's thick plates with a cutout have been studied.The general solution of the stress problem of the thick plate satisfying the boundary conditions on the contour of cutouts is obtained. Applying the orthogonal function expansion technique,the dynamic stress problem can be reduced into the solution of a set of infinite algebraic equations.As examples, numerical results for the dynamic stress concentration factor in Mindlin's plates with a circular,elliptic cutout are graphically presented in sequence.

QUANTITATIVE RELATION BETWEEN YIELD STRESS AND R-VALUE OF Ti PLATE ALONG PARALLEL AND PERPENDICULAR TO ROLLING DIRECTION

An attempt was made on the quantitative prediction of the relationship hetween the yield stress and R-value along the parallel and perpendicular to the rolling direction of Ti plate based on analysis of the previous experimental data.It is shown that the yield stress along one direction and another is quite synchronized with the R—value.According to the plasticity theo- ry,an formular of σ_(1s)/σ_(2s)=[(1+1/R_2)/(1+1/R_1)/^(1 2) was proposed,In statistic estima- tion.the calculated results are in good agreement with the experimental data.The availability of this formula was briefly discussed also.

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.

ANALYSIS OF SYMMETRIC LAMINATED RECTANGULAR PLATES IN PLANE STRESS

Symmetric laminated plates used usually are anisotropic plates. Based on the fundamental equation for anisotropic rectangular plates in plane stress problem, a general analytical solution is established accurately by method of stress function. Therefore the general formula of stress and displacement in plane is given. The integral constants in general formula can be determined by boundary conditions. This general solution is composed of solutions made by trigonometric function and hyperbolic function, which can satisfy the problem of arbitrary boundary conditions along four edges, and the algebraic polynomial solutions which can satisfy the problem of bonndary conditions at four corners. Consequently this general solution can be used to solve the plane stress problem with arbitrary boundary conditions. For example, a symmetric laminated square plate acted with uniform normal load, tangential load and nonuniform normal load on four edges is calculated and analyzed.

Analysis of interlaminar stress and nonlinear dynamic response for composite laminated plates with interfacial damage

By considering the effect of interfacial damage and using the variation principle, three-dimensional nonlinear dynamic governing equations of the laminated plates with interfacial damage are derived based on the general sixdegrees-of-freedom plate theory towards the accurate stress analysis. The solutions of interlaminar stress and nonlinear dynamic response for a simply supported laminated plate with interfacial damage are obtained by using the finite difference method, and the results are validated by comparison with the solution of nonlinear finite element method. In numerical calculations, the effects of interfacial damage on the stress in the interface and the nonlinear dynamic response of laminated plates are discussed.

Stress Analysis of New Type Pre-Stressed Anchor Bearing Plate Combining Stamping with Welding Forming and Its Anchorage Zone

An anchor bearing plate transfers the anchoring force from anchor plate to the concrete and the pre-stress is formed in the concrete structure. Currently, the main type of anchor bearing plate is cast iron. It is brittle during transportation and tension process. This paper presents a new type of anchor bearing plate combined stamping with welding forming. The structure of the new type anchor bearing plate is introduced. The stress states of the anchor bearing plate and anchorage zone under work are studied. Various specifications of anchor bearing plate are studied by ANSYS finite element analysis software following the AASHTO specification. The analysis results are compared with the results of the same type of OVM round-shaped anchor plate. The study results show that the new pre-stressed anchor plates combined stamping with welding forming are feasible and more sturdy which can meet the engineering demand.

A Discussion on Correlations of Plate Motion with Seismic Anisotropy and Stress Field in Plate Boundary Zones

In many parts of the global plates,including subduction zones,mid-ocean ridges and even the interior of the continental plates,seismic anisotropy has a certain correlation with image of absolute plate motion( APM),or is in accord with the predominant direction of the intraplate stress field. In our study,a statistical analysis is done on the correlations of plate motion with seismic anisotropy as well as a stress field within nine plate boundaries which contain major subduction zones in the globe. Results indicate that absolute or relative plate motion( RPM) controls the seismic anisotropy and stress field of the plate boundary,which is especially obvious for the RPM. It can also be inferred that the correlation of RPM is better than that of APM. Because of the complexity of subduction mechanism and diversity of controlling factors at plate boundaries containing subduction zones,the correlation becomes much complex. Sources of anisotropy at various depths show different characteristics,and stress state is controlled by many factors,thus further discussions on the correlations are required.

Numerical investigation on the position of holes for reducing stress concentration in composite plates with bolted and riveted joints

This paper studies the effects of fiber orientaion and holes position on stress concentration and the determination of weakened areas in the composite of glass fiber reinforced epoxy resin around the hole for joints by using the finite element method.In this study,for the observation of areas affected by stress concentration Tsai-Wu failure criterion is used to determine the failed elements and ANSYS Software is implemented for modeling.In order to compare the effect of geometric parameters on stress concentration around the holes,two types of hole position arrangement along with fibers orientation have been studied.Results show that the stress concentration coefficient is lower in the second type of holes arrangement in comparison with the first type for the same component dimensions.Increasing the distance from hole center to upper or lower edge of the sample and also decreasing the distance between holes,would result in an increase in the stress concentration.