The Trefftz finite element method (TFEM) is an efficient numerical approach with many joint advantages of the conventinal finite and boundary element methods. Based on the mutual independent interpolation modes, the finite element formulation involving the boundary integrations only is derived by incorporating the hybrid functional and the Gaussian divergence theorem. The research advances in the internal interpolation function, the treatment of the source term, the special-purpose element and the nonisotropic material during the past decade (2007-2016) are reviewed and several directions are pointed out for the future development.
The normal teeth involve many weak structures, such as pit and fissure, wedge-shaped defect, and cracked tooth. It remains an issue to be explored how to evaluate the effect of these weak structures on the crack initiation and the fracture of the teeth, due to limited evaluation methods. This paper analyzes the failure modes of the dental crown under static and dynamic loads by experimental and numerical methods. It is shown that the weak structures are the determinative factors of the crown fractures, which are in line with the second strength theory. The results of this study will provide a theoretical basis for clinical diagnoses and treatments.
In the problem of linear elasticity of variable stiffness beam, the solution of the deflection curve of static load is usually obtained by integral method or unit-load method. Based on the differential equation of the problem, this paper gives a new type of solution with Green function method to get the deflection curve of the variable stiffness beam. It can be seen from the derivation results that the formulas proposed in this paper have the characteristics of uniformity, accuracy, simplicity and suitable for computerization, which will have important application value for the analysis of the frame structure.
The simplified models of the AFM (atomic force microscope) probe are proposed for a qualitative analysis of dynamic characteristics of the AFM. The forced vibration of the probe is analyzed on the basis of the simplified models. The motion equations are derived based on the models and the wave modes of the AFM probe are obtained by a theoretical calculation. The symmetry problem and the frequency drift are confirmed in the calculation, as consistent with the AFM tests. Meanwhile, an intermittent collision phenomenon is found in the simplified models. The effect of the long-range attractive force on the AFM probe is simulated through a negative spring model.
The 3D printing technology is widely used in medical, aerospace, automotive, construction and other fields. This paper applies a 3D printing technology to the field of rock mechanics experiment. With the 3D printing, two types of gypsum specimens are produced for the laboratory uniaxial compression test, and it is shown that the 3D printing technology can produce the required complex size of the specimens. The 3D printing gypsum specimens enjoy low strength and high plasticity. The mechanical properties of simple standard specimens are found to be reproducible but the mechanical properties of the complex specimens are not; and the production of the specimens with cracks still has technical difficulties.
The finite element static models are validated by considering uncertain factors. The concepts of the correlation and the sensitivity in selecting uncertain parameters are proposed, as well as a general area metric, to validate finite element models. The model of an integrated stiffened panel is used to demonstrate the validation approach. The physical tests of the integrated stiffened panels are carried out to obtain the buckling loads. The finite element model is built with consideration of the stiffened panel and the test-bed. The reliability of the model is assessed against the experimental data by using the area metric. The validation approach in this paper can be used for similar engineering cases.
In the direct shear test, the effect of the gradual decrease of the shear area is not duly considered. The accurate formula of the effective area is derived in this paper. Then, the method of Least Squares is used to deal with the experimental data and it is found that the shear strength error of the soil decreases with the increase of the area of the cutting ring and increases with the shear displacement when the area of the cutting ring is 30 cm2; when the shear displacements are 4 mm and 6 mm, the error is increased as much as 8.2% and 12.38%. The sticky cohesion and the internal friction angle measured by the current method are smaller than the true value, so the shear strength and the parameters of the soil are underestimated and should be corrected.
The duct slide bearing plates are used to reduce the friction force as the duct expands and contracts under temperature variations, but can not be used for seismic isolation without the re-centering capability. In this paper, a double concave friction pendulum system (DCFP) with tri-linear hysteretic behavior is adopted for the gas duct both for thermal displacement and seismic isolation. The seismically isolated duct is modeled as a three-degree-of-freedom system in the transverse direction. The first order state space formulation of the equations of motion is derived, and the theoretical analysis is verified by the finite element analysis. Then the effects of the DCFP on a gas duct and its hysteretic behavior are investigated under various earthquake excitations. Comparing with a duct without the seismic isolation, the reaction force on the DCFP and the shear force on the pier are both greatly reduced.