Cao Zhi-yuan

Non-linear vibration of composite beams with an arbitrary delamination

Abstract In this paper, the non-linear vibration, including the transverse shear, is investigated for composite beams with an arbitrary delamination through the width. The effects of different positions and sizes of the delamination on non-linear vibration of beams are considered. The amplitude–frequency curves of non-linear free vibration are obtained.

The boundary contour method based on the equivalent boundary integral equation for 2-D linear elasticity

The conventional boundary integral equation in two dimensions is non-equivalent to its corresponding boundary value problem when the scale in the fundamental solution reaches its degenerate scale values. An equivalent boundary integral equation was recently derived. This equation has the same solution as the boundary value problem of differential equations. This paper presents the boundary contour method based on the equivalent boundary integral equation for two-dimensional linear elasticity. The method requires only numerical evaluation of potential functions and gives correct equivalent results to the boundary value problem of differential equations in two dimensions. Numerical results are presented for some examples. The present approach is shown to give excellent results in illustrative examples. Meanwhile, the traction results from the BCM based on the conventional displacement boundary integral equation are incorrect.

The traction boundary contour method for linear elasticity

This paper presents a further development of the boundary contour method. The boundary contour method is extended to cover the traction boundary integral equation. A traction boundary contour method is proposed for linear elastostatics. The formulation of traction boundary contour method is regular for points except the ends of the boundary element and corners. The present approach only requires line integrals for three-dimensional problems and function evaluations at the ends of boundary elements for two-dimensional cases. The implementation of the traction boundary contour method with quadratic boundary elements is presented for two-dimensional problems. Numerical results are given for some two-dimensional examples, and these are compared with analytical solutions. This method is shown to give excellent results for illustrative examples. Copyright

The dual boundary contour method for two-dimensional crack problems

This paper concerns the dual boundary contour method for solving two-dimensional crack problems. The formulation of the dual boundary contour method is presented. The crack surface is modeled by using continuous quadratic boundary elements. The traction boundary contour equation is applied for traction nodes on one of the crack surfaces and the displacement boundary contour equation is applied for displacement nodes on the opposite crack surface and noncrack boundaries. The direct calculation of the singular integrals arising in displacement BIEs is addressed. These singular integrals are accurately evaluated with potential functions. The singularity subtraction technique for determining the stress intensity factor KI, KII and the T-term are developed for mixed mode conditions. Some two-dimensional examples are presented and numerical results obtained by this approach are in very good agreement with the results of the previous papers.

LINEAR AND NONLINEAR AERODYNAMIC THEORY OF INTERACTION BETWEEN FLEXIBLE LONG STRUCTURE AND WIND

In light of the characteristics of the interactions between flexible structure and wind in three directions, and based on the rational mechanical section-model of structure, a new aerodynamic force model is accepted, i. e. the coefficients of three component forces are the functions of the instantaneous attack angle and rotational speed Ci=Ci(β(t),ϑ), (i=D, L, M.). So, a new method to formulate the linear and nonlinear aerodynamic items of wind and structure interacting has been put forward in accordance with “strip theory” and modified “quasi-static theory”, and then the linear and nonlinear coupled theory of super-slender structure for civil engineering analyzing are converged in one model. For the linear aerodynamic-force parts, the semi-analytical expressions of the items so-called “flutter derivatives” corresponding to the one in the classic equations have been given here, and so have the nonlinear parts. The study of the stability of nonlinear aerodynamic-coupled torsional vibration of the old Tacoma bridge shows that the form and results of the nonlinear control equation in rotational direction are in agreement with that of V. F. Böhms.

Boundary integral equations of unique solutions in elasticity

The properties of the fundamental solution are derived in linear elastostatics. These properties are used to show that the conventional displacement and traction boundary integral equations yield non-unique displacement solutions in a traction boundary value, problem. The condition for the existence of unique displacement solutions is proposed for the traction boundary value problem. The degrees of freedom of the displacement solution are removed by the condition to obtain the boundary integral equations of unique solutions for the traction boundary value problems. Numerical example is presented to demonstrate the accuracy and efficiency of the present equations.

Dynamic response of underground structures by time domain SBEM and SFEM

The dynamic interaction problems of three-dimensional linear elastic structures with arbitrary shaped section embedded in a homogeneous, isotropic and linear elastic half space under dynamic disturbances are numerically solved. The numerical method employed is a combination of the time domain semi-analytical boundary element method (SBEM) used for the semi-infinite soil medium and the semi-analytical finite element method (SFEM) used for the three-dimensional structure. The two methods are combined through equilibrium and compatibility conditions at the soil-structure interface. Displacements, velocities, accelerations and interaction forces at the interface between underground structure and soil medium produced by the diffraction of wave by an underground structure for every time step are obtained. In dynamic soil-structure interaction problems, it is advantageous to combine the SBEM and the SFEM in an effort to produce an optimum numerical hybrid scheme which is characterized by the main advantages of the two methods. The effects of the thickness, the ratio of length and diameter of underground structure and the soil medium on dynamic responses are discussed.

Elasto-plastic coupled analysis of buried structure and soil medium by perturbational semi-analytic method

In this paper, an effective numerical method for physically nonlinear interaction analysis is studied, in which the elasto-plastic problem of coupled analysis between the structure and medium may be transformed into several linear problems by mean of the perturbation technique, then, the finite strip method and finite layer method are used to analyse the underground structure and rock medium, respectively, for their corresponding linear problems, so the purpose of simplifing the calculation can be achieved. This kind of method has made use of the twice semi-analytical technique: the perturbation and semi-analytic solution function to simplify 3-D nonlinear coupled problem into 1-D linear numerical one. In addition, this method is a new advance of semi-analytical method in the application to nonlinear problems by means of combinating with the analytical perturbation method, and it is also a branch of the perturbational numerical method developed in last years.