Y.Z. Chen

Numerical solution for degenerate scale problem arising from multiple rigid lines in plane elasticity

Abstract This paper studies the degenerate scale problem arising from multiple rigid lines in plane elasticity. In the first step, the problem should be formulated on a degenerate scale by distribution of body force densities along rigid lines. The condition of vanishing displacement along lines is also assumed. The coordinate transform with a reduced factor “ h ” is performed in the next step. The new obtained BIE is a particular non-homogenous BIE defined in the transformed coordinates with normal scale. In the normal scale, the integral operator is invertible. By using two fundamental solutions that are formulated in the normal scale, the new obtained BIE can be reduced to an equation for finding the factor “ h ”. Finally, the degenerate scale is obtained. It is proved from computed results that the degenerate scale only depends on the configuration of rigid lines, and does not depend on the initial normal scale used. In addition, the degenerate scale is invariant with respect to the rotation of rigid lines. Many examples are carried out.

Solution of flat crack problem by using variational principle and differential–integral equation

Abstract Variational principle is used to solve some flat crack problems in three-dimensional elasticity. In the formulation, the strain energy is evaluated by multiplying the crack opening displacement (COD) by the boundary traction. The boundary traction is related to the COD function by a differential–integral representation. By using an integration by part, the portion of the strain energy of the potential functional can be expressed by a repeated integral. In the integral all the integrated functions are non-singular. Letting the functional be minimum, the solution is obtained. In the actual solution, the COD function is represented by a shape function family in which several undetermined coefficients are involved. Using the variational principle, the coefficients are obtained. Several numerical examples are given with the stress intensity factors calculated along the crack border.

Clinical and CT Manifestation of Pleural Schwannoma

Background A schwannoma arising from the pleura is rare. The computer tomography (CT) features, however, have seldom been disclosed in the English literature. Purpose To retrospectively assess the role of CT in the diagnosis of pleural schwannomas. Material and Methods Eleven patients with pathologically confirmed pleural schwannomas were included in the study. CT images and clinical data were analyzed. The CT features emphasized included the location of the neoplasm, as well as its diameter, origin, margin, shape, attenuation, enhancement pattern, and extent and invasion into adjacent structures, all of which were observed and recorded. Results Seven patients were men, while four were women; patients were aged 21-60 years, with a mean age of 45 years. Most cases were incidentally detected. Seven cases involved neoplasms located in the right hemithorax whereas four cases involved neoplasms in the left hemithorax. The mean tumor diameter was 4.4 cm (range, 2.3-6.4 cm). All of the tumors were solitary and well-defined ovoid (n = 7) or round (n = 4) in shape. The schwannomas showed isoattenuation (four cases) or mild hypoattenuation (seven cases) to the chest wall muscle on unenhanced CT. All cases showed minimal enhancement on contrast-medium-enhanced CT. Two bony erosions of the rib were also observed. Conclusion CT findings may suggest the diagnosis of pleural schwannoma preoperatively. Pleural schwannoma should be included in the differential diagnosis of solid, solitary, and well-defined pleural tumors.

Evaluation of the T-stress for multiple cracks in an elastic half-plane using singular integral equation and Green's function method

This paper studies the T-stress problem for multiple cracks in an elastic half-plane using the singular integral equation and Greens function method. In the relevant perturbation field, the boundary of the elastic half-plane is traction free. In the solution, the complex potentials are decomposed into two parts, the principal part and the complementary part. The principal part of the complex potentials is derived from dislocation distributions along the crack faces. The role of the complementary part is to eliminate the traction along the boundary of half-plane caused by the principal part. Finally, a singular integral equation is formulated in which the dislocation distributions are unknown function. The explicit formulae for evaluating the stress intensity factors and the T-stresses at the crack tips are provided. Several numerical examples are presented.

A semi-analytic solution for multiple curved cracks emanating from circular hole using singular integral equation

This paper provides an elastic solution for an infinite plate containing multiple curved edge cracks emanating from a circular hole. A fundamental solution is suggested, which represents a particular solution for a concentrated dislocation in an infinite plate with the traction free hole. The generalized image method and the concept of the modified complex potentials are used in the derivation of the fundamental solution. After using the fundamental solution and placing the distributed dislocations at the prospective sites of cracks, a singular integral equation is formulated. The singular integral equation is solved by using the curve length method in conjunction with the semi-opening quadrature rule. By taking an additional point dislocation at the hole center, the number of the unknowns is equal to the number of the resulting algebraic equations. This is a particular advantage of the suggested method. Finally, several numerical examples are given to illustrate the efficiency of the method presented. Numerical examinations are carried out and sufficient accurate results have been found.

Functional imaging of interstitial brachytherapy in pancreatic carcinoma xenografts using spectral CT: how does iodine concentration correlate with standardized uptake value of (18)FDG-PET-CT?

OBJECTIVE This study aimed to investigate the correlation between iodine concentration (IC) for the quantitative analysis of spectral CT and maximum standardized uptake value (SUVmax) of 18 fludeoxyglucose positron emission tomography-CT ((18)FDG PET-CT) as an indicator of therapeutic response to interstitial brachytherapy in transplanted human pancreatic carcinomas in BALB/c-nu mice. METHODS Xenograft models were created by subcutaneous injection of SW1990 human pancreatic cancer cell suspensions into immunodeficient BALB/c-nu mice. 30 mice bearing SW1990 human pancreatic cancer cell xenografts were randomly separated into two groups: experimental (n = 15; 1.0 mCi) and control (n = 15, 0 mCi). After 2 weeks of treatment, spectral CT and (18)FDG micro-PET-CT scan were performed. IC values and SUVmax in the lesions were measured. IC normalized to the muscle tissue is indicated as nIC. The relationships between the nIC and SUVmax of the transplantation tumours were analysed. RESULTS 2 weeks after treatment, the nIC in three-phase scans and SUVmax of the experimental group were significantly lower than those of the control group. The nIC values of the three-phase scans have certain positive correlation with the SUVmax values (r = 0.69, p < 0.05; r = 0.73 and p < 0.05; r = 0.80, p < 0.05 in the 10-, 25- and 60-s phase, respectively). CONCLUSION Spectral CT could serve as a valuable imaging modality, as our results suggest that nIC correlates with SUVmax of (18)FDG PET-CT for evaluating the therapeutic effect of (125)I interstitial brachytherapy in a pancreatic carcinoma xenograft. ADVANCES IN KNOWLEDGE Spectral CT offers opportunities to assess the therapeutic response of pancreatic cancer. This study supports the conclusion that nIC values in spectral CT could also serve as a valuable functional imaging parameter for early monitoring and evaluation of the therapeutic response of (125)I interstitial brachytherapy mouse models because the nIC correlates with the SUVmax of (18)FDG PET-CT.

Singular integral equation method for contact problem for rigidly connected punches on elastic half-plane

In the contact problem of a rigid flat-ended punch on an elastic half-plane, the contact stress under punch is studied. The angle distribution for the stress components in the elastic medium under punch is achieved in an explicit form. From obtained singular stress distribution, the punch singular stress factor (abbreviated as PSSF) is defined. A fundamental solution for the multiple flat punch problems on the elastic half-plane is investigated where the punches are disconnected and the forces applied on the punches are arbitrary. The singular integral equation method is suggested to obtain the fundamental solution. Further, the contact problem for rigidly connected punches on an elastic half-plane is considered. The solution for this problem can be considered as a superposition of many particular fundamental solutions. The resultant forces on punches are the undetermined unknowns in the problem, which can be evaluated by the condition of relative descent between punches. Finally, the resultant forces on punches can be determined, and the PSSFs at the corner points can be evaluated. Numerical examples are given.

SINGULAR STRESS ANALYSIS IN FLAT PUNCH PROBLEM OF ELASTIC HALF-PLANE

Singular stress analysis in the flat punch problem of half-plane is carried out. The angle distribution for the stress components is also achieved in an explicit form. Followed a similar study in the punch analysis, the punch singular stress factor (abbreviated as PSSF) is defined from the singular stress distribution. For the problems of two punches or three punches, solutions in a closed form are obtained. The obtained solutions may depend on some complete elliptical integrals. Meantime, the exerting location of the resultant force for punches is also determined. Interactions between punches are also addressed. Several numerical examples with the calculated results are presented.

Solution for a crack stiffened by an elliptic layer in antiplane elasticity

This paper provides a solution for a crack stiffened by elliptic layer in antiplane elasticity. The crack is embedded in an elliptic region and stiffened by a confocally elliptic layer. The whole medium is composed of three portions, the cracked elliptic plate, the confocally elliptic layer and the infinite matrix. The remote loading is applied. The cracked elliptic plate and the infinite matrix have the same shear modulus of elasticity. The stiffening elliptic layer has a higher shear modulus of elasticity. By using the complex variable and the continuity conditions along interfaces, the problem can be solved. One numerical example with different sizes and properties of materials is given to show the effect of the stiffening layer.