PDE Standardization Analysis and Solution of TypicalMechanics Problems

A numerical approach is an effective means of solving boundary value problems(BVPs).This study focuses on physical problems with general partial differential equations(PDEs).It investigates the solution approach through the standard forms of the PDE module in COMSOL.Two typical mechanics problems are exemplified:The deflection of a thin plate,which can be addressed with the dedicated finite element module,and the stress of a pure bending beamthat cannot be tackled.The procedure for the two problems regarding the three standard forms required by the PDE module is detailed.The results were in good agreement with the literature,indicating that the PDE module provides a promising means to solve complex PDEs,especially for those a dedicated finite element module has yet to be developed.

Undrained semi-analytical solution for cylindrical cavity expansion in anisotropic soils under biaxial stress conditions

This paper presents an undrained semi-analytical elastoplastic solution for cylindrical cavity expansion in anisotropic soil under the biaxial stress conditions.The advanced simplified SANICLAY model is used to simulate the elastoplastic behavior of soil.The cavity expansion is treated as an initial value problem and solved as a system of eight first-order ordinary differential equations including four stress components and four anisotropic parameters.The results are validated by comparing the new solutions with existing ones.The distributions of stress components and anisotropic parameters around the cavity wall,the expansion process,the stress yield trajectory of a soil element and the shape and size of elastoplastic boundary are further investigated to explore the cavity expansion response of soils under biaxial in situ stresses.The results of extensive parameters analysis demonstrate that the circumferential position of the soil element and the anisotropy of the soils have noticeable impacts on the expansion response under biaxial in situ stresses.Since the present solution not only considers the anisotropy and anisotropy evolution of natural soil,but also eliminates the conventional assumption of uniform radial pressure,the solution is better than other theoretical solutions to explain the pressure test and pile installation effect of shallow saturated soil.

ANALYTICAL SOLUTIONS TO STRESS CONCENTRATION PROBLEM IN PLATES CONTAINING RECTANGULAR HOLE UNDER BIAXIAL TENSIONS

The stress concentration problem in structures with a circular or elliptic hole can be investigated by analytical methods. For the problem with a rectangular hole, only approximate results are derived. This paper deduces the analytical solutions to the stress concentration problem in plates with a rectangular hole under biaxial tensions. By using the U-transformation technique and the finite element method, the analytical displacement solutions of the finite element equations are derived in the series form. Therefore, the stress concentration can then be discussed easily and conveniently. For plate problem the bilinear rectangular element with four nodes is taken as an example to demonstrate the applicability of the proposed method. The stress concentration factors for various ratios of height to width of the hole are obtained.

Symplectic solution for three dimensional couple stress problem and its variational principle

A new state vector is presented for symplectic solution to three dimensional couple stress problem. Without relying on the analogy relationship, the dual PDEs of couple stress problem are derived by a new state vector. The duality solution methodology in a new form is thus extended to three dimensional couple stress. A new symplectic orthonormality relationship is proved. The symplectic solution to couple stress theory based a new state vector is more accordant with the custom of classical elasticity and is more convenient to process boundary conditions. A Hamilton mixed energy variational principle is derived by the integral method.

Measurement of length-scale and solution of cantilever beam in couple stress elasto-plasticity

Owing to the absence of proper analytical solution of cantilever beams for couple stress/strain gradient elasto-plastic theory, experimental studies of the cantilever beam in the micro-scale are not suitable for the determination of material length-scale. Based on the couple stress elasto-plasticity, an analytical solution of thin cantilever beams is firstly presented, and the solution can be regarded as an extension of the elastic and rigid-plastic solutions of pure bending beam. A comparison with numerical results shows that the current analytical solution is reliable for the case of σ0 〈〈 H 〈〈 E, where σ0 is the initial yield strength, H is the hardening modulus and E is the elastic modulus. Fortunately, the above mentioned condition can be satisfied for many metal materials, and thus the solution can be used to determine the material length-scale of micro-structures in conjunction with the experiment of cantilever beams in the micro-scale.

Effects of applied potential on the stress corrosion cracking behavior of 7003 aluminum alloy in acid and alkaline chloride solutions

Potentiodynamic polarization tests and slow strain rate test（SSRT） in combination with fracture morphology observations were conducted to investigate the stress corrosion cracking（SCC） behavior of 7003 aluminum alloy（AA7003） in acid and alkaline chloride solutions under various applied potentials（Ea）. The results show that AA7003 is to a certain extent susceptible to SCC via anodic dissolution（AD） at open-circuit potential（OCP） and is highly susceptible to hydrogen embrittlement（HE） at high negative Ea in the solutions with p H levels of 4 and 11. The susceptibility increases with negative shift in the potential when Ea is less than-1000 m V vs. SCE. However, the susceptibility distinctly decreases because of the inhibition of AD when Ea is equal to-1000 m V vs. SCE. In addition, the SCC susceptibility of AA7003 in the acid chloride solution is higher than that in the alkaline solution at each potential. Moreover, the effect of hydrogen on SCC increases with increasing hydrogen ion concentration.

Pentoxifylline enhances the protective effects of hypertonic saline solution on liver ischemia reperfusion injury through inhibition of oxidative stress

BACKGROUND：Liver ischemia reperfusion（IR）injury triggers a systemic inflammatory response and is the main cause of organ dysfunction and adverse postoperative outcomes after liver surgery.Pentoxifylline（PTX）and hypertonic saline solution（HTS）have been identified to have beneficial effects against IR injury.This study aimed to investigate if the addition of PTX to HTS is superior to HTS alone for the prevention of liver IR injury.METHODS： Male Wistar rats were allocated into three groups. Control rats underwent 60 minutes of partial liver ischemia, HTS rats were treated with 0.4 mL/kg of intravenous 7.5% NaCl 15 minutes before reperfusion, and HPTX group were treated with 7.5% NaC1 plus 25 mg/kg of PTX 15 minutes before reperfusion. Samples were collected after reperfusion for determination of ALT, AST, TNF-α, IL-6, IL-10, mitochondrial respiration, lipid peroxidation, pulmonary permeability and myeloperoxidase. RESULTS： HPTX significantly decreased TNF-α 30 minutes after reperfusion. HPTX and HTS significantly decreased ALT,AST, IL-6, mitochondrial dysfunction and pulmonary myelo- peroxidase 4 hours after reperfusion. Compared with HTS only, HPTX significantly decreased hepatic oxidative stress 4 hours after reperfusion and pulmonary permeability 4 and 12 hours after reperfusion. CONCLUSION： This study showed that PTX added the beneficial effects of HTS on liver IR injury through decreases of hepatic oxidative stress and pulmonary permeability.

The Discrete-Analytical Solution Method for Investigation Dynamics of the Sphere with Inhomogeneous Initial Stresses

The paper deals with a development of the discrete-analytical method for the solution of the dynamical problems of a hollow sphere with inhomogeneous initial stresses.The examinations are made with respect to the problem on the natural vibration of the hollow sphere the initial stresses in which is caused by internal and external uniformly distributed pressure.The initial stresses in the sphere are determined within the scope of the exact equations of elastostatics.It is assumed that after appearing this static initial stresses the sphere gets a dynamical excitation and mechanical behavior of the sphere caused by this excitation is described with the so-called three-dimensional linearized equations of elastic wave propagation in initially stressed bodies.For the solution of these equations,which have variable coefficients,the discrete analytical solution method is developed and applied.In particular,it is established that the convergence of the numerical results with respect to the number of discretization is very acceptable and applicable for the considered type dynamical problems.Numerical results on the influence of the initial stresses on the values of the natural frequencies of the hollow sphere are also presented and these results are discussed.

The Effect of the pH of Ammonum Nitrate Solution on the Susceptability of Mild Steel to Stress Corrosion Cracking (SCC) and General Corrosion

This work investigates the relative aggressiveness of nitrate solutions at different pH values on mild steel towards stress corrosion cracking (SCC) and general corrosion. Electrochemical behavior and stress corrosion cracking sus-ceptibility measurements were carried out in 52 Wt% ammonium nitrate solutions at 368° K and various pH values ranging from 0.77 to 9.64. Constant load stress corrosion test at 90% yield stress was conducted. Tested specimens were prepared and examined using the scanning electron microscope (SEM). The potentiodynamic polarization curves for different pH values again emphasized the validity of the gravimetric measurements and hence the mechanism of cracking was attributed to the stress that assisted the dissolution process.

Stress Field Analysis of Homogeneous Roof by Truss Support Based on Elasticity Mechanics Solution

This paper takes the solution of Boussinesq model, Cerrutl model and Mindlin model as basic solution of elasticity mechanics. on the basis of research conclusion of the accuracy property or rock bolt stress field studied in reference [7], satisfictory elaticity mechanics solution of homogeneous roof rock stress field is given and the rule of stress field change with various parameters is studied.

Oral administration of hyperoxygenated solution for the prophylaxis of gastric ulceration induced by stress or Helicobacter pylori

Oxygen was first discovered by Sweden chemist Scheele in 1773 and convinced as an essential factor for living by French scientists in 1777.To tackle with different hypoxic emergencies,corresponding medical approaches,e.g.mask or nasal catheter oxygen inhalation,breathing machine,hyperbaric oxygen therapy etc.,have been contrived in succession.However,one mortal trouble exists in all these conventional ways,i.e.they must rely on the ventilation and gas exchange via lungs,thus not being able to promptly render oxygen to specific hypoxia tissues.Hyperoxygenated solution(HOS),a new kind of medical liquid which can be orally taken or intravenously administrated,has been widely applied as an auxiliary method of offering oxygen in China.A large number of experiments have proved its validity in the treatment of myocardial and cerebral ischemia/reperfusion injury,nerve lesions,shock,respiratory diseases,neonatal hypoxia and so forth.These findings suggest that HOS might not only play a role of increasing oxygen pressure in local region,but also conspicuously contribute to improving the pathologic process of hypoxia,which coincidently is the vital link in stress-induced lesions in the gastrointestinal tract.Additionally,Helicobacter pylori(H.pylori),a kind of microaerophilic(anaerobic)bacterium which can hardly survive in an aerobic atmosphere,has also been identified as an independent risk factor for the occurrence and development of ulceration.Considering the etiology of peptic ulceration and the features of HOS,we hypothesize that drinking HOS might prevent gastric ulceration caused by stress or anaerobic H.pylori.

ANALYTICAL SOLUTIONS OF THERMAL STRESS DISTRIBUTION IN PLASTIC ENCAPSULATED INTEGRATED CIRCUIT PACKAGES

Due to the mismatch in the coefficients of thermal expansion of slicon chip and the surrounding plastic encapsulation materials, the induced thermal stress is the main cause for die and encapsulant rupture. The corner geometry is simplified as the semi_infinite wedge. Then the two_dimensional thermal stress distribution around the corner was obtained explicitly. Based on the stress calculation, the strain energy density factor criterion is used to evaluate the strength of the structure, which can not only give the critical condition for the stresses, but also determine the direction of fracture initiation around the corner.

Closed form solution of stress intensity factors for cracks emanating from surface semi-spherical cavity in finite body with energy release rate method

In this paper, a new semi-analytical and semi-engineering method of the closed form solution of stress intensity factors （SIFs） of cracks emanating from a surface semi-spherical cavity in a finite body is derived using the energy release rate theory. A mode of crack opening displacements of a normal slice is established, and the normal slice relevant functions are introduced. The proposed method is both effective and accurate for the problem of three-dimensional cracks emanating from a surface cavity. A series of useful results of SIFs are obtained.

FEM analyses for influences of stress-chemical solution on THM coupling in dual-porosity rock mass

The models of stress corrosion,pressure solution and free-face dissolution/precipitation were introduced.Taking a hypothetical nuclear waste repository in an unsaturated dual-porosity rock mass as the calculation objective,four cases were designed:1) the fracture aperture is a function of stress corrosion,pressure solution and free-face dissolution/precipitation;2) the fracture aperture changes with stress corrosion and pressure solution;3) the fracture aperture changes with pressure solution and free-face dissolution/precipitation;4) the fracture aperture is only a function of pressure solution,and the matrix porosity is also a function of stress in these four cases.Then,the corresponding two-dimensional FEM analyses for the coupled thermo-hydro-mechanical processes were carried out.The results show that the effects of stress corrosion are more prominent than those of pressure solution and free-face dissolution/precipitation,and the fracture aperture and relevant permeability caused by the stress corrosion are only about 1/5 and 1/1000 of the corresponding values created by the pressure solution and free-face dissolution/precipitation,respectively.Under the action of temperature field from released heat,the negative pore and fracture pressures in the computation domain rise continuously,and are inversely proportional to the sealing of fracture aperture.The vector fields of flow velocity of fracture water in the cases with and without considering stress corrosion are obviously different.The differences between the magnitudes and distributions of stresses within the rock mass are very small in all cases.

Stress analytical solution for plane problem of a double-layered thick-walled cylinder subjected to a type of non-uniform distributed pressure

The stress state around circular openings,such as boreholes,shafts,and tunnels,is usually needed to be evaluated.Solutions for stresses,strains and ultimate bearing capacities of pressurized hollow cylinder are common cases.Stress analytical method for plane problem of a double-layered thick-walled cylinder subjected to a type of non-uniform pressure on the outer surface and uniform radial pressure on the inner surface is given.The power series method of complex function is used.The stress analytical solution is obtained with the assumption that two layers of a cylinder are fully contacted.The distributions of normal and tangential contact stress along the interface,tangential stress on the inner boundary and stresses in the radial direction at θ=0°,45° and 90°,are obtained.An example indicates that,when the elastic modulus of the inner layer of a double-layered thick-walled cylinder is smaller than that of the outer layer,the tangential stress is smaller than that in the corresponding point for a traditional cylinder composed of homogeneous materials.In that way,stress concentration at the inner surface can be alleviated and the stress distribution is more uniform.This is a capable way to enhance the elastic ultimate bearing capacity of thick-walled cylinder.

Effect of Temperature and Concentration of Ammonium Nitrate Solution on the Succeptibility of Mild Steel to Stress Corrosion Cracking

The effect of varying the temperature and the concentration of ammonium nitrate solution on the stress corrosion cracking (SCC) susceptibility of mild steel is studied. An increase in the temperature causes a decrease in the stress corrosion life. It appears that the susceptibility in the range 368 K to 380 K was greater than at other temperatures. Near the boiling point corrosion and stress corrosion occurs, at the boiling point, the cracking was associated with a high rate of general corrosion. Microscopic examination after stress corrosion testing in 10Wt%, 20Wt%, and 52Wt% NH4NO3 solution revealed that in all cases there was severe intergranular attack, especially at the high concentration.

A CLOSED FORM SOLUTION OF STRESS INTENSITY FACTORS FOR THREE DIMENSIONAL FINITE BODIES WITH ECCENTRIC CRACKS

In this paper, a new analytical-engineering method of closed form solution about stress intensity factors for three dimensional finite bodies with eccentric cracks is derived by means of energy release rate method. The results of stress intensity factors can be obtained. The results provided ir this method are in nice agreement with those of the famous alternating method by which only special cases can be solved.

Exact solutions for different vorticity functions of couple stress fluids

In this paper, inverse solutions are obtained for the class of 2D steady incompressible couple stress fluid flows. This class consists of flows for which the vorticity distribution is given by ▽2ψ=ψ+f(x,y). The solutions are obtained by applying the inverse method, which makes certain hypotheses regarding the form of the velocity field and pressure but without making any regarding the boundaries of the domain occupied by the fluid. Inverse solutions are derived for three different forms of f(x,y).

SOLUTION TO THE STRESS DISTRIBUTION ON THE SURFACE LAYER OF BUSHING ALLOY BY COUPLING BEM WITH ELASTICITY METHOD

In the design of the fatigue strength of dynamically loaded bearing in the equipmentssuch as internal combustion engines and roimg mun, the solution to the stress distribution on thebushing alloy layer is an important and difficult problem. In this paper, a new method has beenproposed by coupling BEM with etheticity method, The algorithm and its implementation were deseribed in details The calculation results verify that this up-dated method can provide us a moresimple and effective tool for solvingthe fatigue stress of the bushing alloy with tangible benefit oftime-saving and high computation accuraey. It may open a new vista in bearing fatigue strength design.

Focal Mechanism Solutions and Stress Field Inversion of Moderately Strong Earthquakes in the Northern Tianshan Area

Using the focal mechanism solutions of 24 moderately strong earthquakes in the northern Tianshan area,we carried out system cluster and stress field inversion analysis.The result indicates that,the focal mechanism solutions of moderately strong earthquakes are mainly dip-slip reverse faulting in the northern Tianshan area.The principal rupture planes of earthquakes are NW-oriented.It is basically consistent with the strike of earthquake structure in its adjacent area.The direction of the principal compression stress P axis is nearly NS,and its inclination angle is small;while the inclination angle of the principal extensional stress T axis is large.It shows that the regional stress field is mainly controlled by the near-NS horizontal compressive stress.The direction of the maximum principal stress shows a gradation process of NNE-NS-NW from east to west.