Amended influence matrix method for removal of rigid motion in the interior BVP for plane elasticity

A conventional complex variable boundary integral equation(CVBIE) in plane elasticity is provided. After using the Somigliana identity between a particular fundamental stress field and a physical stress field, an additional integral equality is obtained. By adding both sides of this integral equality to both sides of the conventional CVBIE, the amended boundary integral equation(BIE) is obtained. The method based on the discretization of the amended BIE is called the amended influence matrix method.With this method, for the Neumann boundary value problem(BVP) of an interior region,a unique solution for the displacement can be obtained. Several numerical examples are provided to prove the efficiency of the suggested method.

GENERAL DYNAMIC EQUATION AND DYNAMICAL CHARACTERISTICS OF VISCOELASTIC TIMOSHENKO BEAMS

In this paper,a governing differential equation of viscoelastic Timoshenko beamincluding both extension and shear viscosity is developed in the time domain by directmethod.To measure the complex moduli and three parameters of standard linear solid,theforced vibration technique of beam is successfully used for PCL and PMMA specimens.The dynamical characteristics of viscoelastic Timoshenko beams,especially the dampingproperties,are derived from a considerable number of numerical computations.Theanalyses show that the viscosity of materials has great influence on dynamicalcharacteristics of structures,especially on damping,and the standard linear solid model isthe better one for describing the dynamic behavior of high viscous materials.

Degenerate scale problem in antiplane elasticity or Laplace equation for contour shapes of triangles or quadrilaterals

This paper provides several solutions to the degenerate scale for the shapes of triangles or quadrilaterals in an exterior boundary value problem (BVP) of the antiplane elasticity or the Laplace equation. The Schwarz-Christoffel mapping is used throughout. It is found that a complex potential with a simple form in the mapping plane satisfies the vanishing displacement condition (or w = 0) along the boundary of the unit circle when the dimension R reaches its critical value 1. This means that the degenerate size in the physical plane is also achieved. The degenerate scales can be evaluated from the particular integrals depending on certain parameters in the mapping function. The numerical results of degenerate sizes for the shapes of triangles or quadrilaterals are provided.

ANTI-PLANE FRACTURE ANALYSIS OF FUNCTIONALLY GRADIENT MATERIAL INFINITE STRIP WITH FINITE WIDTH

The special case of a crack under mode III conditions was treated, lying parallel to the edges of an infinite strip with finite width and with the shear modulus varying exponentially perpendicular to the edges. By using Fourier transforms the problem was formulated in terms of a singular integral equation. It was numerically solved by representing the unknown dislocation density by a truncated series of Chebyshev polynomials leading to a linear system of equations. The stress intensity factor (SIF) results were discussed with respect to the influences of different geometric parameters and the strength of the non-homogeneity. It was indicated that the SIF increases with the increase of the crack length and decreases with the increase of the rigidity of the material in the vicinity of crack. The SIF of narrow strip is very sensitive to the change of the non-homogeneity parameter and its variation is complicated. With the increase of the non-homogeneity parameter, the stress intensity factor may increase, decrease or keep constant, which is mainly determined by the strip width and the relative crack location. If the crack is located at the midline of the strip or if the strip is wide, the stress intensity factor is not sensitive to the material non-homogeneity parameter.

Seismic pounding and collapse behavior of neighboring buildings with different natural periods

Seismic pounding phenomena, particularly the collision of neighboring buildings under long-period ground motion, are becoming a significant issue in Japan. We focused on a specific apartment structure called the Nuevo Leon buildings in the Tlatelolco district of Mexico City, which consisted of three similar buildings built consecutively with narrow expansion joints between the buildings. Two out of the three buildings collapsed completely in the 1985 Mexican earthquake. Using a finite element code based on the adaptively shifted integration (ASI)-Gauss technique, a seismic pounding analysis is performed on a simulated model of the Nuevo Leon buildings to understand the impact and collapse behavior of structures built near each other. The numerical code used in the analysis provides a higher computational efficiency than the conventional code for this type of problem and enables us to address dynamic behavior with strong nonlinearities, including phenomena such as member fracture and elemental contact. Contact release and recontact algorithms are developed and implemented in the code to understand the complex behaviors of structural members during seismic pounding and the collapse sequence. According to the numerical results, the collision of the buildings may be a result of the difference of natural periods between the neighboring buildings. This difference was detected in similar buildings from the damages caused by previous earthquakes. By setting the natural period of the north building to be 25% longer than the other periods, the ground motion, which hada relatively long period of 2 s, first caused the collision between the north and the center buildings. This collision eventually led to the collapse of the centerbuilding, followed by the destruction of the north building.

High intensity focused ultrasound in clinical tumor ablation

Recent advances in high intensity focused ultrasound(HIFU),which was developed in the 1940s as a viable thermal tissue ablation approach,have increased its popularity.In clinics,HIFU has been applied to treat a variety of solid malignant tumors in a well-defined volume,including the pancreas,liver,prostate,breast,uterine fibroids,and soft-tissue sarcomas.In comparison to conventional tumor/cancer treatment modalities,such as open surgery,radio-and chemo-therapy,HIFU has the advantages of non-invasion,non-ionization,and fewer complications after treatment.Over 100 000 cases have been treated throughout the world with great success.The fundamental principles of HIFU ablation are coagulative thermal necrosis due to the absorption of ultrasound energy during transmission in tissue and the induced cavitation damage.This paper reviews the clinical outcomes of HIFU ablation for applicable cancers,and then summarizes the recommendations for a satisfactory HIFU treatment according to clinical experience.In addition,the current challenges in HIFU for engineers and physicians are also included.More recent horizons have broadened the application of HIFU in tumor treatment,such as HIFU-mediated drug delivery,vessel occlusion,and soft tissue erosion(“histotripsy”).In summary,HIFU is likely to play a significant role in the future oncology practice.

AN EDGE CRACK PROBLEM IN A SEMI-INFINITE PLANE SUBJECTED TO CONCENTRATED FORCES

An oblique edge crack problem in a semi-infinite plane is discussed. The concentrated forces are applied on the edge crack face, or on the line boundary of the cracked semi-infinite plane. The rational mapping function approach is suggested to solve the boundary value problem and a solution in a closed form is obtained. Finally, several numerical examples with the calculated results are given.

STRESS ANALYSIS FOR AN INFINITE STRIP WEAKNED BY PERIODIC CRACKS

Stress analysis for an infinite strip weakened by periodic cracks is studied. The cracks were assumed in a horizontal position, and the strip was applied by tension “ p " in y_ direction. The boundary value problem can be reduced into a complex mixed one. It is found that the EEVM ( eigenfunction expansion variational method) is efficient to solve the problem. The stress intensity factor at the crack tip and the T _stress were evaluated. From the deformation response under tension the cracked strip can be equivalent to an orthotropic strip without cracks. The elastic properties in the equivalent orthotropic strip were also investigated. Finally, numerical examples and results were given.

Closed form solution and numerical analysis for Eshelby's elliptic inclusion in plane elasticity

This paper presents a closed form solution and numerical analysis for Eshelby's elliptic inclusion in an infinite plate. The complex variable method and the conformal mapping technique are used. The continuity conditions for the traction and displacement along the interface in the physical plane are reduced to the similar conditions along the unit circle of the mapping plane. The properties of the complex potentials defined in the finite elliptic region are analyzed. From the continuity conditions, one can separate and obtain the relevant complex potentials defined in the inclusion and the matrix. From the obtained complex potentials, the dependence of the real strains and stresses in the inclusion from the assumed eigenstrains is evaluated. In addition, the stress distribution on the interface along the matrix side is evaluated. The results are obtained in the paper for the first time.

EVALUATION OF DEGENERATE SCALE FOR N-GON CONFIGURATION IN ANTIPLANE ELASTICITY

This paper provides a solution for the degenerate scale for N-gon configuration in antiplane elasticity using the conformal mapping function, and the lower and upper bounds for the degenerate scale for N=3,4,5,6,7,8,10,20,30,40,50,100,150 and 200, are evaluated.

New exact solutions for the time fractional coupled Boussinesq-Burger equation and approximate long water wave equation in shallow water

The aim of the article is to construct exact solutions for the time fractional coupled Boussinesq-Burger and approximate long water wave equations by using the generalized Kudryashov method.The fractional differential equation is converted into ordinary differential equations with the help of fractional complex transform and the modified Riemann-Liouville derivative sense.Applying the generalized Kudryashov method through with symbolic computer maple package,numerous new exact solutions are successfully obtained.All calculations in this study have been established and verified back with the aid of the Maple package program.The executed method is powerful,effective and straightforward for solving nonlinear partial differential equations to obtain more and new solutions with the integer and fractional order.