Abstract. Cracks resulting from shrinkage due to temperature or moisture usually exist in the flexible pavements in highways and runways of airport. This paper presents at finite element analysis of 4-layered flexible pavements with a penetrated longitudinal crack on surface layer embedded with controlled low-strength materials (CLSM) bases which are well-known recycling sustainable materials. Two-dimensional deformation assumption is employed. Emphasis is put on the effect of using CLSM bases on the reduction surface settlement, horizontal and vertical stresses as well as crack face displacements. Two kinds of CLSMs, i.e., CLSM-B80/30% and CLSM-B130/30% are compared with graded crushed stones and AC used for base materials. Numerical study shows that vertical settlements, vertical and horizontal stresses by using CLSM-B130/30% base is smaller than that by using graded crushed stone and is shown to be good material employed as base substitute for graded crushed stone in flexible pavement design.

The purpose of this study is to derive an analytical solution for a cantilever beam with a novel spring-like actuator that behaves like a time-dependent spring and to study the dynamic behavior of the system. A time-dependent spring was set at the free end of the cantilever beam to model the novel spring-like actuator. First, the boundary conditions were transformed from being nonhomogeneous to being homogeneous using the shifting function method. The solution of the analytic series was then obtained by using the expansion theorem method. The correctness of the proposed analytical solution was verified by comparing the results with those obtained via the separation of variables in the special extreme case of a constant spring coefficient. We took the free end of a cantilever beam with harmonic spring stiffness and an external periodic unit load as an example. The influence of the actuator parameters, such as the effect of the magnitude and the frequency of the time-dependent spring stiffness on the resonance frequency, was investigated. An important new result was found, i.e., that the resonance frequency is clearly dependent on the magnitude and the frequency of the spring-like actuator in the first two modes, but not in the third and fourth modes. In practical engineering applications, system resonance can be avoided by adjusting the magnitude and frequency of the actuator.

No abstract

This paper proposed a closed-form solution for the 2D transient heat conduction in a rectangular cross-section of an infinite bar with the general Dirichlet boundary conditions. The boundary conditions at the four edges of the rectangular region are specified as the general case of space–time dependence. First, the physical system is decomposed into two one-dimensional subsystems, each of which can be solved by combining the proposed shifting function method with the eigenfunction expansion theorem. Therefore, through the superposition of the solutions of the two subsystems, the complete solution in the form of series can be obtained. Two numerical examples are used to investigate the analytic solution of the 2D heat conduction problems with space–time-dependent boundary conditions. The considered space–time-dependent functions are separable in the space–time domain for convenience. The space-dependent function is specified as a sine function and/or a parabolic function, and the time-dependent function is specified as an exponential function and/or a cosine function. In order to verify the correctness of the proposed method, the case of the space-dependent sinusoidal function and time-dependent exponential function is studied, and the consistency between the derived solution and the literature solution is verified. The parameter influence of the time-dependent function of the boundary conditions on the temperature variation is also investigated, and the time-dependent function includes harmonic type and exponential type.