In this paper a finite element method for free-surface problems is described. the method is based on two different forms of Hamilton's principle. To test the present computational method two specific wave problems are investigated; the dispersion relations and the nonlinear effect for the well-known solitary waves are treated. The convergence test shows that the present scheme is more efficient than other existing methods, e.g. perturbation scheme.

A procedure is formulated, in this paper, to compute the bifurcation modes born by the stability change of normal modes, and to compute the forced responses associated with bifurcation modes in inertially and elastically coupled nonlinear oscillators. It is assumed that a saddle-loop is formed in Poincare map at the stability chage of normal modes. In order to test the validity of procedure, it is applied to one-to-one internal resonant systems in which the solutions are guaranteed within the order of a small perturbation parameter. The procedure is also applied to the exact system in which normal modes are written in exact form and the stability of normal modes can be exactly determined. In this system the stability change of normal modes occurs several times so that various types of bifurcation modes are created. A method is described to identify a fixed point on Poincare map as one of bifurcation modes. The limitations and advantage of proposed procedure are discussed.

The paper attempts to estimate the incubation time of a cavity in the interface between a power law creep particle and an elastic matrix subjected to a uniaxial stress. Since the power law creep particle is time dependent, the stresses in the interface relax. Through previous stress analysis related to the present physical model, the relaxation time is defined by ${\alpha}$2 which satisfies the equation $\Gamma$0 ｜1+${\alpha}$2k｜m=1-${\alpha}$2 [19]. $\Gamma$0=2(1/√3)1+m($\sigma$$\infty$/2${\mu}$)m($\sigma$0/$\sigma$$\infty$tm) where $\sigma$$\infty$ is an applied stress, ${\mu}$ is a shear modulus of a matrix, $\sigma$$\infty$ is a material constant of a power law particle, $\sigma$=$\sigma$0 $\varepsilon$ and t elapsed time. the volume free energy associated with Helmholtz free energy includes strain energies associated with Helmholtz free energy includes strain energies caused by applied stress anddislocations piled up in interface (DPI). The energy due to DPI is found by modifying the results of Dundurs and Mura[20]. The volume free energies caused by both applied stress and DPI are a function of the cavity size(${\gamma}$) and elapsed time(t) and arise from stress relaxation in the interface. Critical radius ${\gamma}$ and incubation time t to maximize Helmholtz free energy is found in present analysis. Also, kinetics of cavity fourmation are investigated using the results obtained by Riede[16]. The incubation time is defied in the analysis as the time required to satisfy both the thermodynamic and kinetic conditions. Through the analysis it is found that [1] strain energy caused by the applied stress does not contribute significantly to the thermodynamic and kinetic conditions of a cavity formation, 2) in order to satisfy both thermodynamic and kinetic conditions, critical radius ${\gamma}$ decreases or holds constant with increase of time until the kinetic condition(eq.40) is satisfied. Therefore the cavity may not grow right after it is formed, as postulated by Harris[11], and Ishida and Mclean[12], 3) the effects of strain rate exponent (m), material constant $\sigma$0, volume fraction of the particle to matrix(f) and particle size on the incubation time are estimated using material constants of the copper as matrix.

An analytical method is presented for predicting the effect of a local deviation in the form of a concentrated mass along a radial line on the free bending vibration characteristics of a nearly axisymmetric circular plate. The approach is based on the Rayleigh-Ritz method and the expression of local deviation of the concentrated radial mass as the variation of heaviside unit step function. The effects of the concentrated mass on the natural frequencies and mode shapes of the plate are predicted with a proposed nondimensional mass parameter.

In this paper, a finite viscoelastic continuum model for rubber and its finite element analysis are presented. This finite viscoelatic model based on continuum mechanics is an extended model of Johnson and Wuigley's 1-D model. In this extended model, continuum based kinematic measures are rigorously defied and by using this kinematic measures, elastic stage law and flow rule are introduced. In kinematics, three configuration are introduced. In kinematics, three configuration are introduced. They are reference, current and virtual visco configurations. In elastic state law, it is assumed that at a certain time, there exists an elastic potential which describes the recoverable elastic energy. From this elastic potential, elastic state law is derived. The proposed flow rule is based on phenomenological observation. The flow rule gives precise relaxation response. In finite element approximation, mixed Lagrangian description is used, where total and similar method of updated Lagrangian descriptions are used together. This approach reduces the numerical job and gives simple nonlinear syatem of equations. To satisfy the incompressible condition, penalty-type modified Mooney-Rivlin energy function is adopted. By this method nearly incompressible condition is obtain the virtual visco configuration. For verification, uniaxial stretch tests are simulated for various stretch rates. The simulated results show good agreement with experiments. As a practical experiments. As a preactical example, pressurized rubber plate is simulated. The result shows finite viscoelastic effects clearly.