T. Fujimoto¹ and T. Nishioka¹

CMES-Computer Modeling in Engineering & Sciences, Vol.11, No.2, pp. 91-102, 2006, DOI:10.3970/cmes.2006.011.091

Abstract In the dynamic fracture of metallic material, some cracks propagate with the incidence of plastic deformation, and distinct plastic strain remains near the post-propagation area. In order to elucidate these dynamic nonlinear fracture processes, the moving finite element method is developed for nonlinear crack propagation. The T* integral is used as the parameter to estimate crack tip condition. First, the effect of material viscosity and crack propagation velocity have been discussed based on the numerical results for fracture under pure mode I high speed loading. Under mixed mode loading, numerical simulations for fracture path prediction are demonstrated for various crack… More >

T. Yoda¹, N. Kodama²

CMES-Computer Modeling in Engineering & Sciences, Vol.11, No.1, pp. 1-8, 2006, DOI:10.3970/cmes.2006.011.001

Abstract A nonlinear dynamic response analysis of a box section steel rigid frame under seismic action is proposed on the basis of a beam model. The average stress-strain relation of the beam model can be formulated for transverse stiffener spacing, in which stress-strain relation after local buckling is assumed. As a result of the present study, the maximum lateral displacements and the residual displacements of a box section steel rigid frame were well estimated by the proposed beam element model that considers the deterioration effect due to local buckling. More >

Q.W. Ma¹

CMES-Computer Modeling in Engineering & Sciences, Vol.9, No.2, pp. 193-210, 2005, DOI:10.3970/cmes.2005.009.193

Abstract Recently, the MLPG (Meshless Local Petrov-Galerkin Method) method has been successfully extended to simulating nonlinear water waves [Ma, (2005)]. In that paper, the author employed the Heaviside step function as the test function to formulate the weak form over local sub-domains, acquiring an expression in terms of pressure gradient. In this paper, the solution for Rankine sources is taken as the test function and the local weak form is expressed in term of pressure rather than pressure gradient. Apart from not including pressure gradient, velocity gradient is also eliminated from the weak form. In addition, a semi-analytical technique is developed… More >

M. Akamatsu¹, K. Nakane², N. Ohno^1,2

CMES-Computer Modeling in Engineering & Sciences, Vol.10, No.3, pp. 217-228, 2005, DOI:10.3970/cmes.2005.010.217

Abstract In this study, a fully implicit integration scheme is developed for a nonisothermal viscoplastic, nonlinear kinematic hardening model. Nonlinear dynamic recovery in addition to strain hardening is assumed for the evolution of multiple back stresses so that ratcheting and mean-stress relaxation can be properly simulated. Temperature dependence of back stress evolution is also taken into account in the constitutive model. By discretizing a set of such advanced constitutive relations using the backward Euler method, a tensor equation is derived and linearized to iteratively achieve the implicit integration of constitutive variables. The fully implicit integration scheme developed is programmed as a… More >

Z. D. Han¹, A. M. Rajendran², S.N. Atluri¹

CMES-Computer Modeling in Engineering & Sciences, Vol.10, No.1, pp. 1-12, 2005, DOI:10.3970/cmes.2005.010.001

Abstract A nonlinear formulation of the Meshless Local Petrov-Galerkin (MLPG) finite-volume mixed method is developed for the large deformation analysis of static and dynamic problems. In the present MLPG large deformation formulation, the velocity gradients are interpolated independently, to avoid the time consuming differentiations of the shape functions at all integration points. The nodal values of velocity gradients are expressed in terms of the independently interpolated nodal values of displacements (or velocities), by enforcing the compatibility conditions directly at the nodal points. For validating the present large deformation MLPG formulation, two example problems are considered: 1) large deformations and rotations of… More >

S. Okamoto¹, Y. Omura¹

CMES-Computer Modeling in Engineering & Sciences, Vol.4, No.2, pp. 287-300, 2003, DOI:10.3970/cmes.2003.004.287

Abstract The purpose of this study is to develop a procedure for performing a dynamic analysis in the case that a structure undergoes large translational and rotational displacements when moving along a nonlinear trajectory at variable velocity. Finite-element equations of motion that include the inertial force of the structure's motion have been derived. The equations also account for the geometric nonlinearity that has to be considered in a problem of finite translational and rotational displacements. A finite rotational matrix was used to transfer vectors or matrices measured in a certain coordinate frame to those measured in another coordinate frame. The computational… More >

Wen Yi Lin¹, Kuo Mo Hsiao²

CMES-Computer Modeling in Engineering & Sciences, Vol.4, No.2, pp. 259-272, 2003, DOI:10.3970/cmes.2003.004.259

Abstract The buckling and postbuckling behavior of spatial rods under different types of end torque and compressive axial force is investigated using finite element method. All coupling among bending, twisting, and stretching deformations for beam element is considered by consistent second-order linearization of the fully geometrically nonlinear beam theory. However, the third order term of the twist rate is also considered. An incremental-iterative method based on the Newton-Raphson method combined with constant arc length of incremental displacement vector is employed for the solution of nonlinear equilibrium equations. The zero value of the tangent stiffness matrix determinant of the structure is used… More >

K. Ijima¹, H. Obiya¹, S. Iguchi², S. Goto²

CMES-Computer Modeling in Engineering & Sciences, Vol.4, No.2, pp. 239-248, 2003, DOI:10.3970/cmes.2003.004.239

Abstract Defining element coordinates in space frame, element end deformations become statically clear from the energy principle. Therefore, the deformations can be expressed by nodal displacement without any approximation. The paper indicates that the exact expressions of the deformations and the geometrical stiffness strictly based on the equations makes large displacement analysis of space frame possible with robustness on the computation. More >

K.Yu. Volokh¹

CMES-Computer Modeling in Engineering & Sciences, Vol.2, No.3, pp. 389-400, 2001, DOI:10.3970/cmes.2001.002.389

Abstract A computational framework is described for modeling pin-jointed structures comprising unilateral cable members and slender struts. The deep postbuckling behavior of struts is considered by means of 'elastica' analytical approximation. Prestressing is allowed. The proposed approach is incorporated into equilibrium path following procedures and illustrated in numerical examples. More >

KwangsooHo¹

CMES-Computer Modeling in Engineering & Sciences, Vol.2, No.3, pp. 351-364, 2001, DOI:10.3970/cmes.2001.002.351

Abstract Negative, zero or positive rate sensitivity of the flow stress can be observed in metals and alloys over a certain range of strain, strain rate and temperature. It is believed that negative rate sensitivity is an essential feature of dynamic strain aging, of which the Portevin-Le Chatelier effect is one other manifestation. The viscoplasticity theory based on overstress (VBO), one of the unified state variable theories, is generalized to model zero (rate independence) and negative as well as positive rate sensitivity in a consistent way. The present model does not have the stress rate term in the evolution law for… More >