• Journal of Ocean Engineering and Technology
• /
• v.25 no.4
• /
• pp.36-41
• /
• 2011

In the present paper, a direct forcing/fictitious domain (DF/FD) level set method is proposed to simulate the FSI (fluid-solid interaction) in two-phase flow. The main idea is to combine the direct-forcing/fictitious domain (DF/FD) method with the level set method in the Cartesian coordinates. The DF/FD method is a non-Lagrange-multiplier version of a distributed Lagrange multiplier/fictitious domain (DLM/FD) method. This method does not sacrifice the accuracy and robustness by employing a discrete ${\delta}$ (Dirac delta) function to transfer quantities between the Eulerian nodes and Lagrangian points explicitly as the immersed boundary method. The advantages of this approach are the simple concept, easy implementation, and utilization of the original governing equation without modification. Simulations of various water-entry problems have been conducted to validate the capability and accuracy of the present method in solving the FSI in two-phase flow. Consequently, the present results are found to be in good agreement with those of previous studies.

• Transactions of the Korean Society of Mechanical Engineers
• /
• v.17 no.10
• /
• pp.2457-2466
• /
• 1993

A simple method is presented for determining transient responses of locally nonlinear structures using substructure eigenproperties and Lagrange multiplier technique. Although the method is based upon the mode synthesis formulation procedure, the equations of the combined whole structure are not constructed compared with the conventional methods. Lagrange multi-pliers are used to enforce the conditions of geometric compatibility between the substructure interfaces and they are treated as external forces on each substructure itself. Substructure eigenvalue problem is defined with the substructure interface free of fixed. The transient analysis is based upon the recurrence discrete-time state equations and offers the simplicity of the Euler integration method without requiring small time increment and iterative solution procedure. Numerical examples reveal that the method is very accurated and efficient in calculating transient responses compared with the direct numerical integration method.

• The Transactions of the Korean Institute of Electrical Engineers A
• /
• v.48 no.8
• /
• pp.958-964
• /
• 1999

The distance in load parameter space to the closest saddle node bifurcation (CSNB) point provides the worst case power margin to voltage instability and the left eigenvector at CSNB identifies the most effective direction to steer the system to maximize voltage stability under contingency. This paper presents an improved direct method for computing CSNB: the order of nonlinear systems equations is reduced to about twice of the size of load flow equations in contrast to about three-times in Dobson's direct method; the initial guess for the direct method is computed efficiently and robustly by combined use of continuation power flow, a pair of multiple load flow solution with Lagrange interpolation. It is also shown that voltage stability may be enhanced significantly with shift of generations in the direction of the left eigenvector at CSNB.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 1993.04a
• /
• pp.52-56
• /
• 1993

An efficient method is presented for determining transient responses of locally nonlinear structures using substructure eigenproperties and Lagrange multiplier technique. The method is based upon the mode synthesis formulation procedure, but does not construct the equations of motion of the combined whole structure compared with the conventional methods. For modal bases of each linear substructure, either fixed or free interface modes can be employed. The transient analysis is based upon the recurrence discrete-time state equations and offers the simplicity of the Euler integration method without requiring small time increment and iterative solution procedure. Numerical examples reveal that the method is very accurate and efficient in calculating transient responses compared with the direct numerical integration method.

• Journal of KSNVE
• /
• v.8 no.5
• /
• pp.887-899
• /
• 1998

It has been resulted that Lagrange multiplier method with statistical approach was superior to traditional harmonic balance method in identifying the nonlinear loudspeaker parameters when output signals were contaminated with Gaussian random noise. We have known that the displacement-dependent characteristic values of nonlinear parameters identified by traditional harmonic balance method were estimated less than original values by the increase of output noise and the stiffness coefficients were very sensitive to output noise. Also, by the sensitivity analysis we have verified that the harmonic distortions in acoustic radiation was mainly due to nonlinearity of force factor caused by uneven magnetic fields and that reducing the nonlinearity of damping coefficients were very effective for improving second harmonic distrotion of acoustic radiation.

• Smart Structures and Systems
• /
• v.16 no.5
• /
• pp.853-872
• /
• 2015

Numerical analysis of large amplitude free vibration behaviour of laminated composite spherical shell panel embedded with the piezoelectric layer is presented in this article. For the investigation purpose, a general nonlinear mathematical model has been developed using higher order shear deformation mid-plane kinematics and Green-Lagrange nonlinearity. In addition, all the nonlinear higher order terms are included in the present mathematical model to achieve any general case. The nonlinear governing equation of freely vibrated shell panel is obtained using Hamilton's principle and discretised using isoparametric finite element steps. The desired nonlinear solutions are computed numerically through a direct iterative method. The validity of present nonlinear model has been checked by comparing the responses to those available published literature. In order to examine the efficacy and applicability of the present developed model, few numerical examples are solved for different geometrical parameters (fibre orientation, thickness ratio, aspect ratio, curvature ratio, support conditions and amplitude ratio) with and/or without piezo embedded layers and discussed in details.

• Steel and Composite Structures
• /
• v.18 no.3
• /
• pp.693-709
• /
• 2015

In this article, nonlinear free vibration behaviour of functionally graded spherical panel is analysed. A nonlinear mathematical model is developed based on higher order shear deformation theory for shallow shell by taking Green-Lagrange type of nonlinear kinematics. The material properties of functionally graded material are assumed to be varying continuously in transverse direction and evaluated using Voigt micromechanical model in conjunction with power-law distribution. The governing equation of the shell panel is obtained using Hamilton's principle and discretised with the help of nonlinear finite element method. The desired responses are evaluated through a direct iterative method. The present model has been validated by comparing the frequency ratio (nonlinear frequency to linear frequency) with those available published literatures. Finally, the effect of geometrical parameters (curvature ratio, thickness ratio, aspect ratio and support condition), power law indices and amplitude of vibration on the frequency ratios of spherical panel have been discussed through numerical experimentations.

• Journal of the Computational Structural Engineering Institute of Korea
• /
• v.35 no.5
• /
• pp.249-257
• /
• 2022

This paper presents an improved computational framework for the direct-solution-based finite element tearing and interconnecting (FETI) algorithm. The FETI-local algorithm is further improved herein, and localized Lagrange multipliers are used to define the interface among its subdomains. Selective inverse entry computation, using a property of the Boolean matrix, is employed for the computation of the subdomain interface stiffness and load, in which the original FETI-local algorithm requires a full matrix inverse computation of a high computational cost. In the global interface computation step, the original serial computation is replaced by a parallel multi-frontal method. The performance of the improved FETI-local algorithm was evaluated using a numerical example with 64 million degrees of freedom (DOFs). The computational time was reduced by up to 97.8% compared to that of the original algorithm. In addition, further stable and improved scalability was obtained in terms of a speed-up indicator. Furthermore, a performance comparison was conducted to evaluate the differences between the proposed algorithm and commercial software ANSYS using a large-scale computation with 432 million DOFs. Although ANSYS is superior in terms of computational time, the proposed algorithm has an advantage in terms of the speed-up increase per processor increase.

• International Journal of Aeronautical and Space Sciences
• /
• v.16 no.2
• /
• pp.177-189
• /
• 2015

This paper presents an all-direct domain decomposition approach for large-scale structural analysis. The proposed approach achieves computational robustness and efficiency by enforcing the compatibility of the displacement field across the sub-domain boundaries via local Lagrange multipliers and augmented Lagrangian formulation (ALF). The proposed domain decomposition approach was compared to the existing FETI approach in terms of the computational time and memory usage. The parallel implementation of the proposed algorithm was described in detail. Finally, a preliminary validation was attempted for the proposed approach, and the numerical results of two- and three-dimensional problems were compared to those obtained through a dual-primal FETI approach. The results indicate an improvement in the performance as a result of the implementing the proposed approach.

• Structural Engineering and Mechanics
• /
• v.53 no.4
• /
• pp.661-679
• /
• 2015

In this article, nonlinear finite element solutions of bending responses of functionally graded spherical panels are presented. The material properties of functionally graded material are graded in thickness direction according to a power-law distribution of volume fractions. A general nonlinear mathematical shallow shell model has been developed based on higher order shear deformation theory by taking the geometric nonlinearity in Green-Lagrange sense. The model is discretised using finite element steps and the governing equations are obtained through variational principle. The nonlinear responses are evaluated through a direct iterative method. The model is validated by comparing the responses with the available published literatures. The efficacy of present model has also been established by demonstrating a simulation based nonlinear model developed in ANSYS environment. The effects of power-law indices, support conditions and different geometrical parameters on bending behaviour of functionally graded shells are obtained and discussed in detail.