Development of a Three-Dimensional Multiscale Octree SBFEM for Viscoelastic Problems of Heterogeneous Materials

The multiscale method provides an effective approach for the numerical analysis of heterogeneous viscoelastic materials by reducing the degree of freedoms(DOFs).A basic framework of the Multiscale Scaled Boundary Finite Element Method(MsSBFEM)was presented in our previous works,but those works only addressed two-dimensional problems.In order to solve more realistic problems,a three-dimensional MsSBFEM is further developed in this article.In the proposed method,the octree SBFEM is used to deal with the three-dimensional calculation for numerical base functions to bridge small and large scales,the three-dimensional image-based analysis can be conveniently conducted in small-scale and coarse nodes can be flexibly adjusted to improve the computational accuracy.Besides,the Temporally Piecewise Adaptive Algorithm(TPAA)is used to maintain the computational accuracy of multiscale analysis by adaptive calculation in time domain.The results of numerical examples show that the proposed method can significantly reduce the DOFs for three-dimensional viscoelastic analysis with good accuracy.For instance,the DOFs can be reduced by 9021 times compared with Direct Numerical Simulation(DNS)with an average error of 1.87%in the third example,and it is very effective in dealing with three-dimensional complex microstructures directly based on images without any geometric modelling process.

Mode-based equivalent multi-degree-of-freedom system for one-dimensional viscoelastic response analysis of layered soil deposit

Discrete models such as the lumped parameter model and the finite element model are widely used in the solution of soil amplification of earthquakes. However, neither of the models will accurately estimate the natural frequencies of soil deposit, nor simulate a damping of frequency independence. This research develops a new discrete model for onedimensional viscoelastic response analysis of layered soil deposit based on the mode equivalence method. The new discrete model is a one-dimensional equivalent multi-degree-of-freedom（MDOF） system characterized by a series of concentrated masses, springs and dashpots with a special configuration. The dynamic response of the equivalent MDOF system is analytically derived and the physical parameters are formulated in terms of modal properties. The equivalent MDOF system is verified through a comparison of amplification functions with the available theoretical solutions. The appropriate number of degrees of freedom（DOFs） in the equivalent MDOF system is estimated. A comparative study of the equivalent MDOF system with the existing discrete models is performed. It is shown that the proposed equivalent MDOF system can exactly present the natural frequencies and the hysteretic damping of soil deposits and provide more accurate results with fewer DOFs.

DYNAMIC BEHAVIOR ANALYSIS OF VISCOELASTICALLY DAMPED STRUCTURES

Analysis method for the dynamic behavior of viscoelastically damped structures is studied.A finite element model of sandwich beams with eight degrees of freedom is set up and the finite element formulation of the equations of motion is given for the viscoelastically damped structures.An iteration method for solving nonlinear eigenvalue problems is suggested to analyze the dynamic behavior of viscoelastically damped structures. The method has been applied to the complex model analysis of a sandwich cantilever beam with viscoelastic damping material core.

Structural optimization of elliptical-tip star propellant grain using sub-problem approximation

A method is presented here for structural optimization of elliptical-tip star grain.The grain structural integrity was improved by minimizing the most critical area of inner bore hoop strain during cool down.Optimization was done by sub-problem approximation method in conjunction with finite element analysis.Both radii of the ellipse were varied during optimization to find the optimal ellipse.The optimization resulted in grain geometry having minimum level of Inner bore hoop strain without violating the preset limits of burning perimeter.The von mises strain at grain inner bore was also reduced in resultant grain.