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In this paper, the equivalent mechanical spring model of the three-dimensional continuum is studied. By using stiffness calculation formulas of three-dimensional continuum column under axial force and bending force, which are primary force states in the column, a mechanical equivalent trusses model with the same width and height is derived. The equivalent model is statically indeterminate trusses system of spring. The 3D spring calculation model can be used in the dynamic characteristic analysis. With the comparison of the first four order frequency values between the solid model and the equivalent spring model, it shows that the equivalent spring model not only have the equivalent stiffness in the static analysis but also have the equivalent dynamic characteristics in the dynamic analysis.

A simple and efficient explicit scheme of triangular planar element with rotation degrees of freedom is proposed in this paper. The basic fundamental solutions of plane elasticity problem based on Airy stress functions are used as trial functions to construct triangular element with drilling degrees of freedom. During the construction of element model, the explicit expression of element stiffness matrix is deduced by means of triangular area coordinates integration method, instead of numerical integration method. Numerical calculation indicates that the element constructed in this paper is of high precision but less computational cost.

Keywords: Equivalent spring element method; Additional mass method; Dynamic characteristics Abstract. In order to study the effect of fluid on the structural dynamic characteristics, in this paper, a three-dimensional spring element was applied to the dynamic analysis of the fluid. Based on the simplified model of nuclear power structure, the upper water tank of concrete containment was analyzed in different water level by equivalent spring element method and additional mass method. The theory of three-dimensional equivalent spring element was put forward, and then the numerical simulation of different water tank was carried out. The computational results of the two methods showed that the equivalent spring element method and the additional mass method have the similar accuracy.

This paper presents a novel way to calculate the characteristic solutions of the anisotropy V-notch plane problem. The material eigen equation of the anisotropy based on the Stroh theory and the boundary eigen equation of the V-notch plane problem are studied separately. A modified Müller method is utilized to calculate characteristic solutions of anisotropy V-notch plane problem, which are employed to formulate the analytical trial functions (ATF) in the associated finite element method. The numerical examples show that the proposed subregion accelerated Müller method is an efficient method to calculate the solutions of the equation involving the complex variables. The proposed element ATF-VN based on the analytical trial functions, which contain the characteristic solutions of the anisotropy V-notch problem, presents good performance in the benchmarks.