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In this paper, numerical solution of the singular integral equation for the multiple curved branch-cracks is investigated. If some quadrature rule is used, one difficult point in the problem is to balance the number of unknowns and equations in the solution. This difficult point was overcome by taking the following steps: (a) to place a point dislocation at the intersecting point of branches, (b) to use the curve length method to covert the integral on the curve to an integral on the real axis, (c) to use the semi-open quadrature rule in the integration. After taking these steps, the number of the unknowns is equal to the number of the resulting algebraic equations. This is a particular advantage of the suggested method. In addition, accurate results for the stress intensity factors (SIFs) at crack tips have been found in a numerical example. Finally, several numerical examples are given to illustrate the efficiency of the method presented.

In this paper, elastic analysis for a thick cylinder made of functionally graded materials (FGMs) is carried out. The property of FGMs is assumed to be exponential function form. The problem is reduced to solve an ordinary differential equation numerically. Stress distributions along the radial direction are studied. The obtained result shows that the property of FGMs has a significant influence to the stress distribution along the radial direction. Numerical results are given which are useful for engineer to design a cylinder made of FGMs. Similar analysis for spherical pressure vessel made of FGMs is presented.

T-stress dependence on the loading along the crack face is an important topic in fracture analysis. It is found that a statement for T-stress evaluation in Engng Fract Mech 69, 959–981 (2002) is incorrect. A rigorous derivation for T-stress for a semi-infinite crack is presented.

This paper investigates the dependence of the stress intensity factor (abbreviated as SIF) and T-stress from the imposed boundary conditions. A rectangular cracked plate is subject to a tension in the vertical direction. In the first boundary condition, the tension loading is applied at the tops of plate. In the second boundary condition, the relevant assumed displacement is applied on the edges of plate. In the study, the complex potentials are assumed in the series form with undetermined coefficients, and those coefficients can be evaluated by using the variational principle. The aim of study is to obtain the SIF and T-stress at the crack tips for two different boundary conditions. Finally, numerical results are presented. The obtained results may have their application in the fatigue test of a cracked component.

In this paper, a convenient technique for evaluating angular frequency in some nonlinear oscillations is proposed. It is well known that once the restoring force function is given beforehand, the period of motion can be determined by an integral. The angular frequency has a relation with the period of motion as well as the integral. One makes a little modification for the integrand in the integral and a change of variable. It is found that if the three divisions are chosen on the integration interval and the trapezoid quadrature rule is used, a higher accurate result for the angular frequency can be achieved. For the restoring force being an odd function, three numerical examples are presented. The eardrum-type oscillation is studied as well. Higher accurate results for the angular frequency are obtained in all those examples.

In this paper, elastic analysis for an edge‐cracked plate of functionally graded materials (FGMs) is carried out. The cracked plate is subject to a longitudinal tension. The property of FGMs is assumed to be exponential function form in both x‐ and y‐directions. The finite element method is suggested to solve the boundary value problem. An indirect method, the energy release method, is developed to evaluate the stress intensity factors (SIFs) at the crack tip. Under the applied loading, the amount of the release energy from the crack length “a” to “ a + Δa ” can be evaluated from relevant displacements at the top face of plate. The SIFs can be obtained from a relation between the energy release rate and SIF. The obtained result shows that the property of FGMs has a significant influence to the value of SIF at crack tip. Numerical results are given which are useful for engineer to assess the safety of the cracked plate of FGMs.

Three numerical solution techniques for nonlinear eardrum-type oscillations with an even function in the restoring force are studied. The first suggested technique is named the target function technique. In the technique, the second zeros of the target function is the circular frequency of motion. The second suggested technique is named the multiple-parameter technique, and the involved parameters are evaluated from the governing equation, the initial conditions, and properties of motion. The third suggested technique is named the direct integration technique. All techniques depend on the computer computation significantly and provide very accurate numerical results. Finally, numerical examples are given.

In plane elasticity, a general expression for a mutual work difference integral (MWDI) derived from two stress fields is introduced. Once two physical stress fields are known beforehand, the relevant MWDI can be evaluated exactly from the coefficients in the complex potentials. A biaxial tension model for evaluating defect energy is introduced. A particular MWDI from two fields, one is for the damaged medium under remote biaxial tension and other is for an infinite perfect plate under the same remote biaxial tension, can be defined as a suitable measure of stiffness for the damaged medium, which is called the defect energy ( E (a) ). The suggested model can deal with the cracks, holes, and elastic inclusions in a unique way. The model can also evaluate the defect energies for different damages exactly without dependence on the orientation of damages. Physically, the higher is the defect energy achieved, the more are the involved damages in the medium. The defect energy may be negative, which means a more ...

This paper investigates periodic group crack problems in an infinite plate. The periodic group crack is composed of infinite groups with numbering from j = −∞, …, −2, −1, 0, 1, 2, …, to j = ∞, and the groups are placed periodically. The same loading condition and the same geometry are assumed for cracks in all groups. A singular integral equation is used to solve the problems. The singular integral equation is formulated on cracks of the 0th group (or the central group) with the collection of influences from the infinite groups. The influences of many neighboring groups to the central group are evaluated exactly. Meantime, the influences of many remote groups to the central group can be summed up into one term approximately. The stress intensity factors at crack tips can be evaluated from the solution of the singular integral equation. It is found from some sample problems that the obtained results are very accurate. Finally, several numerical examples are presented and interaction among the group cracks is addressed.

Four types (DD1, DD2, FD1 and FD2) of complex potential are introduced in this paper. All types are obtained by distributing the dislocation doublet or force doublet along a plane curve. If the axis of dislocation doublet is placed in the tangential (normal) direction of curve, the DD1 (DD2) type of complex potential is obtainable. Similarly, if the axis of force doublet is placed in the tangential (normal) direction of curve, the FD1 (FD2) type of complex potential is obtainable. The continuous and discontinuous behaviors of the displacement and the resultant force function for four types of complex potential are discussed. It is found that: (a) the complex potential of the type DD1 can model the curve crack problem, (b) the complex potential of the type FD1 can model the curve rigid line problem, (c) the complex potential of the type DD1 can be obtained by a superposition of the types FD1 and FD2, (d) the complex potential of the type FD1 can be obtained by a superposition of the types DD1 and DD2. In this paper, the dislocation doublet (the force doublet) is abbreviated as DD (FD), respectively.