AN APPROACH TO THE ELASTIC-PLASTIC ANALYSIS OF THE PLANE STRAIN MODE-I CRACK

This paper presents an approach to the solution of the approximate elastic-plastic analysis for the plane strain mode-1 crack.

The Stress Analysis for Notched Specimen of Brittle Material under Plane Dead Loading

The stress distribution of notched specimen of brittle material under a plane pressure was studied using a photoelastic meth- od,When elastic deformation appeared inside the specimen,the force transferred by dowel part was triangular transverse force and frictional force on the upper surface of the sample.The quantity of the frictional force was about 31 percent of transverse force.The stress inside the sample was linear along the central cross section of the sample and there was maximum tensile stress σ_y at the tip of the notch.Basing on shearing stress deviation method,the tensile stress σ_y,σ_x and shearing stress τ_(xy) at the cen- tral sections and four adjacent cross sections were calculated.The result pointed out that σ_x and τ_(xy) were smaller than σ_y.There- fore,σ_y was the main factor for crack formation and propagation.

The occlusal plane in the facial context:inter-operator repeatability of a new three-dimensional method

The repeatability of a non-invasive digital protocol proposed to evaluate the three-dimensional（3D） position of the occlusal plane in the face is assessed.Dental virtual models and soft tissue facial morphology of 20 adult subjects were digitally integrated using a 3D stereophotogrammetric imaging system.The digital 3D coordinates of facial and dental landmarks were obtained by two different operators.Camper＇s（facial） and occlusal（dental） planes were individuated,and their 3D relationships were measured.The repeatability of the protocol was investigated and showed no significant differences in repeated digitizations.The angle between occlusal and Camper＇s planes was smaller than 26 in the frontal and horizontal projections.In the sagittal projection,the angle was observed to be,on average,4.9 6.The determined occlusal plane pitch,roll and yaw values show good agreement with previously published data obtained by different protocols.The current non-invasive method was repeatable,without inter-operator differences and can facilitate assessment of healthy subjects.

The use of the greater trochanter marker in the thigh segment model:Implications for hip and knee frontal and transverse plane motion

Background:The greater trochanter marker is commonly used in 3-dimensional(3D) models;however,its influence on hip and knee kinematics during gait is unclear.Understanding the influence of the greater trochanter marker is important when quantifying frontal and transverse plane hip and knee kinematics,parameters which are particularly relevant to investigate in individuals with conditions such as patellofemoral pain,knee osteoarthritis,anterior cruciate ligament(ACL) injury,and hip pain.The aim of this study was to evaluate the effect of including the greater trochanter in the construction of the thigh segment on hip and knee kinematics during gait.Methods:3D kinematics were collected in 19 healthy subjects during walking using a surface marker system.Hip and knee angles were compared across two thigh segment definitions(with and without greater trochanter) at two time points during stance:peak knee flexion(PKF) and minimum knee flexion(Min KF).Results:Hip and knee angles differed in magnitude and direction in the transverse plane at both time points.In the thigh model with the greater trochanter the hip was more externally rotated than in the thigh model without the greater trochanter(PKF:-9.34°± 5.21° vs.1.40°± 5.22°,Min KF:-5.68°± 4.24° vs.5.01°± 4.86°;p < 0.001).In the thigh model with the greater trochanter,the knee angle was more internally rotated compared to the knee angle calculated using the thigh definition without the greater trochanter(PKF:14.67°± 6.78° vs.4.33°± 4.18°,Min KF:10.54°± 6.71° vs.-0.01°± 2.69°;p < 0.001).Small but significant differences were detected in the sagittal and frontal plane angles at both time points(p < 0.001).Conclusion:Hip and knee kinematics differed across different segment definitions including or excluding the greater trochanter marker,especially in the transverse plane.Therefore when considering whether to include the greater trochanter in the thigh segment model when using a surface markers to calculate 3D kinematics for movement assessment,it is important to have a clear understanding of the effect of different marker sets and segment models in use.

Dynamical Analysis on Traveling Wave of a Reaction-Advection-Diffusion Equation with Double Free Boundaries

This paper investigates a reaction-advection-diffusion equation with double free boundaries.The stationary solution of the system is studied by phase plane analysis.Then,the scale logarithm change sequence method is introduced to show the exact heteroclinic of the system with corresponding parameters.Moreover,a complete description of the types of traveling wave solutions is given with different advection term coefficients.

Electron-acoustic supernonlinear waves and their multistability in the framework of the nonlinear Schrödinger equation

Finite-amplitude supernonlinear electron-acoustic waves(EAWs)are investigated under the nonlinear Schrödinger(NLS)equation in a plasma system that is composed of cold electronfluid,immobile ions and q-nonextensive hot electrons.Using the wave transfiguration,the NLS equation is deduced in a dynamical system.The presence of finite-amplitude nonlinear and supernonlinear EAWs is shown by phase plane analysis.The effects of the nonextensive parameter(q)and the speed of waves(v)on different traveling wave solutions of EAWs are presented.Furthermore,by introducing a small external periodic force in the dynamical system,multistability behaviors of EAWs under the NLS equation are shown for the first time in classical plasmas.