A theory is proposed to derive the resultant elastic potential energy change in the systems accompanying phase transformation for a finite concentration of inclusions. Based on the thermodynamic equilibrium, this elastic potential energy due to the interaction of ellipsoidal inclusions is employed to evaluate the critically applied stress that induces phase transformation. It is shown that the material system with the disc inclusions is easier to get the stress-induced transformation than that with other shapes. The inclusions with 3-D random orientation are the most effective one to have toughness increments. The height of the transformation zone strongly depends on the volume concentration and the shape of the inclusions. As compared with the experimental data, the theory is in an acceptable range of accuracy.

Based on a landmark paper by Pao and Gajewski, some novel developments of the method of generalized ray integrals are discussed. The expansion of the dynamic Green's function of the infinite space into plane waves allows benchmark 3-D solutions in the layered half-space and even enters the background formulation of elastic-viscoplastic wave propagation. New developments of software of combined symbolic-numerical manipulation and parallel computing make the method a competitive solution technique.

The reciprocal identity which connects two elastodynamic states, denoted by A and B, is used in this paper to obtain two results for an elastic layer. The first is an orthogonality condition for wave modes. For that case the states A and B are wave modes propagating in the same direction. The second result concerns reflection and transmission of wave motion by an obstacle in the layer. Now state A is defined by a superposition of incident wave modes and its reflection and transmission by the obstacle. Expressions for the reflection and transmission coefficients are obtained by selecting counter propagating wave modes for state B. It is also shown that the reflection by an obstacle in a layer can be extended to obtain the reflection and transmission coefficients for a planar array of obstacles in an unbounded elastic solid. For clarity all results are presented for horizontally polarized transverse wave motion.

Upon encountering a wet or contaminated floor, people often modify their gait and posture to prevent themselves from slipping. This study was conducted to investigate the modification of gait patterns in healthy young adults as they approached and stepped on a slippery floor. Ten females and twelve males were instructed to walk at two different pacer speeds, 90 and 120steps/min, guided by a metronome, on a walkway with two forceplates placed at the center. During the step immediately prior to stepping on a forceplate with or without slippery disturbance, temporo-spatial parameters, selected kinematic parameters, and foot-floor reaction forces were evaluated in each cadence. The results showed that modifications of gait patterns for slip perturbation included shorter step length, increases of flexion angles of hip and knee joints,increases of plantarflexion angles of ankle joint with flattened foot, and decreases of the forward and backward groundreaction forces. However, it was found that such modifications for slip perturbation did not seem to efficiently prevent people from falling.

1. Figures 13 to 18 should be deleted from the paper.

2. The first sentence on page 118, “The corresponding and traction field at r = 1, 10 and 20 for the case of m = 0 are depicted in Figs. 12(a), (b) and (c),” should be modified as: “The corresponding radiation patterns of displacement and traction field at ksr = 1, 10 and 20 for the case of m = 0 are depicted in Figs. 12(a), (b) and (c), respectively.”

During the last decade, we have applied MEMS-based transducers to develop a technology for maneuvering aircraft by sensing and controlling the separation around the leading edge of a delta wing. In this paper, we will summarize our experience of this endeavor.

This paper deals with a hybrid finite element method for wave scattering problems in infinite domains. Scattering of waves involving complex geometries, in conjunction with infinite domains is modeled by introducing a mathematical boundary within which a finite element representation is employed. On the mathematical boundary, the finite element representation is matched with a known analytical solution in the infinite domain in terms of fields and their derivatives. The derivative continuity is implemented by using a slope constraint. Drilling degrees of freedom at each node of the finite element model are introduced to make the numerical model more sensitive to the transverse component of the elastodynamic field. To verify the effects of drilling degrees freedom and slope constraints individually, reflection of normally incident P and SV waves on a traction free half space is considered. For P-wave incidence, the results indicate that the use of a slope constraint is more effective because it suppresses artificial reflection at the mathematical boundary. For the SV-wave case, the use of drilling degrees of freedom is effective in reducing numerical error at the irregular frequencies.

In this paper, a modified version of the method of steepest descent is proposed for the evaluation of Lamb's integrals which can be considered as basis functions dealing with the development of the transition matrix method which can be used to study the wave scattering in a two-dimensional elastic half-space. The formal solutions of the generalized Lamb's problem are studied and evaluated on the basis of the proposed method. After defining a phase function which presents in wavenumber integral, an exact mapping and an inverse mapping can be obtained according to the phase function. Thus, the original integration path can be deformed into an equivalent admissible path, namely, steepest descent path which passed through the saddle point, and then mapped onto a real axis of mapping plane, finally, resulted in an integral of Hermite type. This integral can be efficiently evaluated numerically in spite of either near- to far-field or low to high frequency. At the same time, the asymptotic value can easily be obtained by applying the proposed method. The numerical results for generalized Lamb's solutions are calculated and compared with analytic, asymptotic or other existing data, the excellent agreements are found. The properties of generalized Lamb's solutions are studied and discussed in details. Their possible applications for wave scattering in elastic half-space are also pointed out.

In Section 2, ROTATION OF COORDINATES, the Authors derived the emittance functions in the Weyl-Sommerfeld representation of the wave potentials for a horizontal instantaneous single force from those known for a vertical force from conditions of invariance of the phase and amplitude of plane waves under coordinate rotation, Eqs. (10) ∼ (13) and (18) ∼ (20). That transformation implies the validity of the commonly applied identity for the (force) vector components when rotating the vector in the opposite sense to the coordinate rotation. Further, in the three-dimensional case, the vertical force poses an axisymmetric problem which is compatible with the Fourier transformation applied to the coordinates in the horizontal plane.