This paper will report on the investigation results of the influence of observation errors on the identification of external loads in case of the bending problem of a beam. It is found that the resultant force and the resultant moment of the loads will be conserved despite of the divergence of the identified load distribution, when the observation errors are within a certain tolerance. This fact is applicable to the problem of identifying a small defect.

The solution of heat transfer problems for functional graded materials (FGMs) by smoothed particle hydrodynamics, in which the thermal conductivity is a function of the spatial coordinates and the temperature, is discussed for both steady and non-steady problems under various boundary conditions. The boundary is treated using the corrective smoothed particle method to heighten the accuracy. Several calculations are performed to test the validity of the formulation. As an example of practical application, the problem of FGM cylindrical plates subjected to thermal shock is calculated, in which the thermal conductivity is temperature dependent and the heat transfer coefficient is varied in radial direction.

In the present study, the problem of functionally graded materials (FGMs) under a stress pulse is analyzed based on smoothed particle hydrodynamics (SPH) using the formulation for large deformation. First, the formulation of SPH for this problem is described, and a benchmark calculation is performed and compared to one-dimensional analytical solutions. The behavior of FGMs subjected to a stress pulse is then investigated for several cases, including various distributions of inhomogeneous materials and two-dimensional problems with different boundary conditions. It is found that in the two-dimensional case, if there is a free boundary not parallel to the direction of the external force, the influence from this boundary cannot be ignored.

This paper will propose an identification algorithm for a small defect in the case of the bending problem of a beam. That is to say, the part where a defect exists is replaced by an equivalent load term. It shows that the defect can be accurately identified even there is observation error if the problem of identifying a defect is converted to that of identifying a load.

A formulation using the deviatoric stress and the continuity equation is extended to the analysis of the dynamic response of functionally graded materials (FGMs) subjected to a thermal shock by smoothed particle hydrodynamics (SPH), in which temperature dependent properties of materials are considered. Several dynamic thermal stress problems are analyzed to investigate the fluctuation of thermal stress at the initial stage under three types of thermal conditions, with the addition of two kinds of mechanical boundary conditions.