• Structural Engineering and Mechanics
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• v.45 no.5
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• pp.613-629
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• 2013

In this article we will present a method to directly evaluate the critical point of a non-linear system by using the solution of a polynomial eigenvalue approximation as a starting point for an iterative non-linear system solver. This method will be used to evaluate out-of-plane buckling properties of truss structures for which the lateral displacement of the upper chord has been prevented. The aim is to assess for a number of example structures whether or not the linearized eigenvalue solution gives a relevant starting point for an iterative non-linear system solver in order to find the minimum positive critical load.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.2 no.1
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• pp.27-39
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• 1998

We describe a fast numerical method for non-separable elliptic equations in self-adjoin form on irregular adaptive domains. One of the most successful results in numerical PDE is developing rapid elliptic solvers for separable EPDEs, for example, Fourier transformation methods for Poisson problem on a square, however, it is known that there is no rapid elliptic solvers capable of solving a general nonseparable problems. It is the purpose of this paper to present an iterative solver for linear EPDEs in self-adjoint form. The scheme discussed in this paper solves a given non-separable equation using a sequence of solutions of Poisson equations, therefore, the most important key for such a method is having a good Poison solver. High performance is achieved by using a fast high-order adaptive Poisson solver which requires only about 500 floating point operations per gridpoint in order to obtain machine precision for both the computed solution and its partial derivatives. A few numerical examples have been presented.

• International Journal of Naval Architecture and Ocean Engineering
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• v.3 no.1
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• pp.20-26
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• 2011

A weakly nonlinear seakeeping methodology for predicting motions and loads is presented in this paper. This methodology assumes linear radiation and diffraction forces, calculated in the frequency domain, and fully nonlinear Froude-Krylov and hydrostatic forces, evaluated in the time domain. The particular approach employed here allows to overcome numerical problems connected to the determination of the impulse response functions. The procedure is divided into three consecutive steps: evaluation of dynamic sinkage and trim in calm water that can significantly influence the final results, a linear seakeeping analysis in the frequency domain and a weakly nonlinear simulation. The first two steps are performed employing a three-dimensional Rankine panel method. Nonlinear Froude-Krylov and hydrostatic forces are computed in the time domain by pressure integration on the actual wetted surface at each time step. Although nonlinear forces are evaluated into the time domain, the equations of motion are solved in the frequency domain iteratively passing from the frequency to the time domain until convergence. The containership S175 is employed as a test case for evaluating the capability of this methodology to correctly predict the nonlinear behavior related to wave induced motions and loads in head seas; numerical results are compared with experimental data provided in literature.