• Korean Journal of Materials Research
• /
• v.25 no.2
• /
• pp.81-89
• /
• 2015

A strain-gradient crystal plasticity constitutive model was developed in order to predict the Hall-Petch behavior of a Ni-base polycrystalline superalloy. The constitutive model involves statistically stored dislocation and geometrically necessary dislocation densities, which were incorporated into the Bailey-Hirsch type flow stress equation with six strength interaction coefficients. A strain-gradient term (called slip-system lattice incompatibility) developed by Acharya was used to calculate the geometrically necessary dislocation density. The description of Kocks-Argon-Ashby type thermally activated strain rate was also used to represent the shear rate of an individual slip system. The constitutive model was implemented in a user material subroutine for crystal plasticity finite element method simulations. The grain size dependence of the flow stress (viz., the Hall-Petch behavior) was predicted for a Ni-base polycrystalline superalloy NIMONIC PE16. Simulation results showed that the present constitutive model fairly reasonably predicts 0.2%-offset yield stresses in a limited range of the grain size.

• 한국금형공학회:학술대회논문집
• /
• 2008.06a
• /
• pp.121-127
• /
• 2008

Nowdays CAE has been used for almost all injection molding designs in order to find the best injection conditions. Almost all CAE use 2-D mesh, but the CAE with 2-D mesh can't indicate such as jetting, flow-mark and filling imbalance in multi cavity mold. In this study, we suggested a new 3D meshing. the method which can indicate the filling imbalance in geometrically balanced runner system with Mold Flow MPI 6.1 and we found out that the calculation times are saved. As a feasibility study, we verified that Melt Flipper, RC Pin etc appeared the balanced filling behaviors. of geometrically balanced runner system and Melt Flipper, filling imbalance was indicated more accurately.

• Smart Structures and Systems
• /
• v.18 no.1
• /
• pp.155-181
• /
• 2016

In the present paper we discuss the stability and the post-buckling behaviour of thin piezoelastic plates. The first part of the paper is concerned with the modelling of such plates. We discuss the constitutive modelling, starting with the three-dimensional constitutive relations within Voigt's linearized theory of piezoelasticity. Assuming a plane state of stress and a linear distribution of the strains with respect to the thickness of the thin plate, two-dimensional constitutive relations are obtained. The specific form of the linear thickness distribution of the strain is first derived within a fully geometrically nonlinear formulation, for which a Finite Element implementation is introduced. Then, a simplified theory based on the von Karman and Tsien kinematic assumption and the Berger approximation is introduced for simply supported plates with polygonal planform. The governing equations of this theory are solved using a Galerkin procedure and cast into a non-dimensional formulation. In the second part of the paper we discuss the stability and the post-buckling behaviour for single term and multi term solutions of the non-dimensional equations. Finally, numerical results are presented using the Finite Element implementation for the fully geometrically nonlinear theory. The results from the simplified von Karman and Tsien theory are then verified by a comparison with the numerical solutions.

• Journal of the Computational Structural Engineering Institute of Korea
• /
• v.13 no.2
• /
• pp.209-220
• /
• 2000

For non-linear analysis of stiffened shell structures, the total Lagrangian formulation is presented based upon the degenerated shell element. Geometrically correct formulation is developed by updating the direction of normal vectors and taking into account second order rotational terms in the incremental displacement field. Assumed strain concept is adopted in order to overcome shear locking phenomena and to eliminate spurious zero energy mode. The post-buckling behaviors of stiffened shell structures are traced by modeling the stiffener as a shell element and considering general transformation between the main structure and the stiffener at the connection node. Numerical examples to demonstrate the accuracy and the effectiveness of the proposed shell element are presented and compared with references' results.

• Computational Structural Engineering
• /
• v.10 no.1
• /
• pp.213-223
• /
• 1997

In the analysis of the behavior of a complex structure, it requires much time and cost to analyze its behavior by using shell elements at the early design concept. For the purpose of the decrease of time and cost, many researches have been performed with the intention to analyze its behavior through replacing a shell model by a simple beam model. In the present study, a method is proposed for determining a bending spring stiffness which means the flexibility for applying into the joints of the simple beam model. Geometrically nonlinear analysis is performed through the application of the determined flexibility into joints of the simple beam model. The nonlinear behavior of thin-walled tube shell structure can be described within a little error through the simple beam model with flexible joints.

• Structural Engineering and Mechanics
• /
• v.54 no.3
• /
• pp.433-451
• /
• 2015

This paper focuses on large deflection static behavior of edge cracked simple supported beams subjected to a non-follower transversal point load at the midpoint of the beam by using the total Lagrangian Timoshenko beam element approximation. The cross section of the beam is circular. The cracked beam is modeled as an assembly of two sub-beams connected through a massless elastic rotational spring. It is known that large deflection problems are geometrically nonlinear problems. The considered highly nonlinear problem is solved considering full geometric non-linearity by using incremental displacement-based finite element method in conjunction with Newton-Raphson iteration method. There is no restriction on the magnitudes of deflections and rotations in contradistinction to von-Karman strain displacement relations of the beam. The beams considered in numerical examples are made of Aluminum. In the study, the effects of the location of crack and the depth of the crack on the non-linear static response of the beam are investigated in detail. The relationships between deflections, end rotational angles, end constraint forces, deflection configuration, Cauchy stresses of the edge-cracked beams and load rising are illustrated in detail in nonlinear case. Also, the difference between the geometrically linear and nonlinear analysis of edge-cracked beam is investigated in detail.

• Journal of the Society of Naval Architects of Korea
• /
• v.28 no.2
• /
• pp.307-317
• /
• 1991

A displacement-based finite element method is presented for the geometrically nonlinear analysis of eccentrically stiffened plates. The nonlinear degenerated shell and eccentric isobeam(isoparametric beam) elements are formulated on the basis of total Lagrangian and updated Lagrangian descriptions. To describe the stiffener's local plate buckling mode, some additional local degrees of freedom are used in the eccentric isobeam element. The eccentric isobeam element can be affectively employed to model the eccentric stiffener just like the case of the degenerated shell element. A detailed nonlinear analysis including the effects of stiffener's eccentricity is performed to estimate the critical load and the post buckling behaviour of an eccentrically stiffened plate. The critical buckling loads are found higher than analytic plate buckling load but lower than Euler buckling load which are the buckling strength requirements of classification society.

• Current Applied Physics
• /
• v.18 no.11
• /
• pp.1205-1211
• /
• 2018

The frustrated magnet has been regarded as a system that could be a promising host material for the quantum spin liquid (QSL). However, it is difficult to determine the spin configuration and the corresponding mechanism in this system, because of its geometrical frustration (i.e., crystal structure and symmetry). Herein, we systematically investigate one of the geometrically frustrated magnets, the $TbB_4$ compound. Using resonant soft x-ray scattering (RSXS), we explored its spin configuration, as well as Tb's quadrupole. Comprehensive evaluations of the temperature and photon energy/polarization dependences of the RSXS signals reveal the mechanism of spin reorientation upon cooling down, which is the sophisticated interplay between the Tb spin and the crystal symmetry rather than its orbit (quadrupole). Our results and their implications would further shed a light on the search for possible realization of QSL.

• Structural Engineering and Mechanics
• /
• v.40 no.2
• /
• pp.257-277
• /
• 2011

In this paper the geometrically nonlinear continuum plate finite element model, hitherto not reported in the literature, is developed using the total Lagrange formulation. With the layerwise displacement field of Reddy, nonlinear Green-Lagrange small strain large displacements relations (in the von Karman sense) and linear elastic orthotropic material properties for each lamina, the 3D elasticity equations are reduced to 2D problem and the nonlinear equilibrium integral form is obtained. By performing the linearization on nonlinear integral form and then the discretization on linearized integral form, tangent stiffness matrix is obtained with less manipulation and in more consistent form, compared to the one obtained using laminated element approach. Symmetric tangent stiffness matrixes, together with internal force vector are then utilized in Newton Raphson's method for the numerical solution of nonlinear incremental finite element equilibrium equations. Despite of its complex layer dependent numerical nature, the present model has no shear locking problems, compared to ESL (Equivalent Single Layer) models, or aspect ratio problems, as the 3D finite element may have when analyzing thin plate behavior. The originally coded MATLAB computer program for the finite element solution is used to verify the accuracy of the numerical model, by calculating nonlinear response of plates with different mechanical properties, which are isotropic, orthotropic and anisotropic (cross ply and angle ply), different plate thickness, different boundary conditions and different load direction (unloading/loading). The obtained results are compared with available results from the literature and the linear solutions from the author's previous papers.

• Steel and Composite Structures
• /
• v.33 no.2
• /
• pp.261-275
• /
• 2019

The main objective of this paper is to study the axial buckling and post-buckling of geometrically imperfect single-layer graphene sheets (GSs) under in-plane loading in the theoretical framework of the nonlocal strain gradient theory. To begin with, a graphene sheet is modeled by a two-dimensional plate subjected to simply supported ends, and supposed to have a small initial curvature. Then according to the Hamilton's principle, the nonlinear governing equations are derived with the aid of the classical plate theory and the von-karman nonlinearity theory. Subsequently, for providing a more accurate physical assessment with respect to the influence of respective parameters on the mechanical performances, the approximate analytical solutions are acquired via using a two-step perturbation method. Finally, the authors perform a detailed parametric study based on the solutions, including geometric imperfection, nonlocal parameters, strain gradient parameters and wave mode numbers, and then reaching a significant conclusion that both the size-dependent effect and a geometrical imperfection can't be ignored in analyzing GSs.