• Structural Engineering and Mechanics
• /
• v.62 no.6
• /
• pp.695-702
• /
• 2017

In this work, a nonlocal zeroth-order shear deformation theory is developed for the nonlinear postbuckling behavior of nanoscale beams. The beauty of this formulation is that, in addition to including the nonlocal effect according to the nonlocal elasticity theory of Eringen, the shear deformation effect is considered in the axial displacement within the use of shear forces instead of rotational displacement like in existing shear deformation theories. The principle of virtual work together of the nonlocal differential constitutive relations of Eringen, are considered to obtain the equations of equilibrium. Closed-form solutions for the critical buckling load and the amplitude of the static nonlinear response in the postbuckling state for simply supported and clamped clamped nanoscale beams are determined.

• Journal of the Korean Society for Advanced Composite Structures
• /
• v.3 no.2
• /
• pp.1-10
• /
• 2012

In the present study, an Element-Based Lagrangian Formulation for the nonlinear analysis of shell structures is presented. The strains, stresses and constitutive equations based on the natural co-ordinate have been used throughout the Element-Based Lagrangian Formulation of the present shell element which offers an advantage of easy implementation compared with the traditional Lagrangian Formulation. The Element-Based Lagrangian Formulation of a 9-node resultant-stress shell element is presented for the anisotropic composite material. The element is free of both membrane and shear locking behavior by using the assumed natural strain method such that the element performs very well in thin shell problems. The arc-length control method is used to trace complex equilibrium paths in thin shell applications. Numerical examples for laminated composite curved shells presented herein clearly show the validity of the present approach and the accuracy of the developed shell element.

• Journal of the Korean Mathematical Society
• /
• v.53 no.1
• /
• pp.161-185
• /
• 2016

We consider a mathematical model which describes the quasistatic frictional contact between a piezoelectric body and an electrically conductive obstacle, the so-called foundation. A nonlinear electro-viscoelastic constitutive law is used to model the piezoelectric material. Contact is described with Signorini's conditions and a version of Coulomb's law of dry friction in which the adhesion of contact surfaces is taken into account. The evolution of the bonding field is described by a first order differential equation. We derive a variational formulation for the model, in the form of a system for the displacements, the electric potential and the adhesion. Under a smallness assumption which involves only the electrical data of the problem, we prove the existence of a unique weak solution of the model. The proof is based on arguments of time-dependent quasi-variational inequalities, differential equations and Banach's fixed point theorem.

• Proceedings of the Korean Society for Technology of Plasticity Conference
• /
• 2003.10b
• /
• pp.43-46
• /
• 2003

Prediction of final microstructures after high temperature forming of Ti-6Al-4V alloy was attempted in this study. Using two typical microstructures, i.e., equiaxed and $Widmanst\ddot{a}tten$ microstructures, compression test was carried out up to the strain level of 0.6 at various temperatures $(700\~1100^{\circ}C)$ and strain rates $(10^{-4}\~10^2/s)$. From the flow stress-strain data, parameters such as strain rate sensitivity (m) and activation energy (Q) were calculated and used to establish constitutive equations for both microstructures. Then, finite element analysis was performed to predict the final microstructure of the deformed body, which was well accorded with the experimental results.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.33 no.12
• /
• pp.1366-1374
• /
• 2009

Anterior cruciate ligament(ACL) of human body experiences a large deformation. May during everyday when large deformation is repeated by various activities such as outdoor activity, ACL easily get damaged. In order to acknowledge the effect of the cyclic large deformation to ACL, the constitutive equations for ACL are derived from experiment data. The concept of the objective stress rate plays a important role wherever large deformation occurs. In order to obtain the objective stress rates the eigenprojection technique is used. A comparison is made for four different cases: Jaumann rate, Green-Naghdi rate, logarithmic rate and twirl tensor of Eulerian triad rate for an isotropic material subject to cyclic deformation, such as simple shear motion. Four different materials are studied to compare the behavior of the materials for ACL using different objective rates. Finally, more complicated model with fibers for soft tissues is used to calculate the behavior subjected to cyclic large deformation.

• Structural Engineering and Mechanics
• /
• v.18 no.6
• /
• pp.807-829
• /
• 2004

The Element-Based Lagrangian Formulation of a 9-node resultant-stress shell element is presented for the isotropic and anisotropic composite material. The effect of the coupling term between the bending strain and displacement has been investigated in the warping problem. The strains, stresses and constitutive equations based on the natural co-ordinate have been used throughout the Element-Based Lagrangian Formulation of the present shell element which offers an advantage of easy implementation compared with the traditional Lagrangian Formulation. The element is free of both membrane and shear locking behavior by using the assumed natural strain method such that the element performs very well in thin shell problems. In composite plates and shells, the transverse shear stiffness is defined by an equilibrium approach instead of using the shear correction factor. The arc-length control method is used to trace complex equilibrium paths in thin shell applications. Several numerical analyses are presented and discussed in order to investigate the capabilities of the present shell element. The results showed very good agreement compared with well-established formulations in the literature.

• Computers and Concrete
• /
• v.19 no.5
• /
• pp.501-507
• /
• 2017

The predictive utility of a damage model depends heavily on its particular choice of a damage variable, which serves as a macroscopic approximation in describing the underlying micromechanical processes of microdefects. In the case of spatially perfectly randomly distributed microcracks or microvoids in all directions, isotropic damage model is an appropriate choice, and scalar damage variables were widely used for isotropic or one-dimensional phenomenological damage models. The simplicity of a scalar damage representation is indeed very attractive. However, a scalar damage model is of somewhat limited use in practice. In order to entirely characterize the isotropic damage behaviors of damaged materials in multidimensional space, a system theory of isotropic double scalar damage variables, including the expressions of specific damage energy release rate, the coupled constitutive equations corresponding to damage, the conditions of admissibility for two scalar damage effective tensors within the framework of the thermodynamics of irreversible processes, was provided and analyzed in this study. Compared with the former studies, the theoretical formulations of double scalar damage variables in this study are given in the form of matrix, which has many features such as simpleness, directness, convenience and programmable characteristics. It is worth mentioning that the above-mentioned theoretical formulations are only logically reasonable. Owing to the limitations of time, conditions, funds, etc. they should be subject to multifaceted experiments before their innovative significance can be fully verified. The current level of research can be regarded as an exploratory attempt in this field.

• Steel and Composite Structures
• /
• v.36 no.3
• /
• pp.293-305
• /
• 2020

This article presented a nanoscale modified continuum model to investigate the free vibration of functionally graded (FG) porous nanobeam by using finite element method. The main novelty of this manuscript is presenting effects of four different porosity models on vibration behaviors of nonlocal nanobeam structure including size effect, that not be discussed before The proposed porosity models are, uniform porosity distribution, symmetric with mid-plane, bottom surface distribution and top surface distribution. The nano-scale effect is included in modified model by using the differential nonlocal continuum theory of Eringen that adding the length scale into the constitutive equations as a material parameter constant. The graded material is distributed through the beam thickness by a generalized power law function. The beam is simply supported, and it is assumed to be thin. Therefore, the kinematic assumptions of Euler-Bernoulli beam theory are held. The mathematical model is solved numerically using the finite element method. Results demonstrate effects of porosity type, material gradation, and nanoscale parameters on the free vibration of nanobeam. The proposed model is effective in vibration analysis of NEMS structure manufactured by porous functionally graded materials.

• Transactions of Materials Processing
• /
• v.12 no.8
• /
• pp.710-717
• /
• 2003

The implicit, finite element analysis program for analyzing the springback in the warm forming process of aluminum alloy sheets was developed. For the description of planar anisotropy in warm forming temperatures, Barlat's yield function is employed, and the power law type constitutive equation is used in terms of working temperatures for the depiction of work hardening in high temperatures. Also, Jetture's 4-node shell elements are introduced for reflecting the mechanical behavior of aluminum alloy sheet and the non-steady heat balance equations are solved for considering heat gain and loss during the forming process. For the springback evaluation, Newton-Raphson iteration method is introduced for overcoming the geometric nonlinearlity problem. In order to verify the validity of the FEM program developed, the stretching bending and springback processes are simulated. Though springback analysis results are slightly bigger than experimental ones, they have the same trend of the decreasing springback as the forming temperature increases.

• Journal of the Korean Geotechnical Society
• /
• v.27 no.3
• /
• pp.95-102
• /
• 2011

A model of solid-water-air coupling in triphasic mixture is compared to that of solid-water coupling in biphasic mixture with an application to partially saturated soils. Based on thermodynamics, the mathematical framework governing the behavior of a partially saturated soil is derived by using balance equations, and numerical implementation through drainage experiment of a sand column is carried out to validate the obtained formulations. The role of the air phase in the hydro-mechanical behavior of triphasic mixture can be analyzed from the interaction among phases and from the solid skeleton's constitutive behavior, and the three-phase model found applications in geotechnical engineering problems, such as $CO_2$ sequestration and air storage in an aquifer.