Strong-form framework for solving boundary value problems with geometric nonlinearity

In this paper, we present a strong-form framework for solving the boundary value problems with geometric nonlinearity, in which an incremental theory is developed for the problem based on the Newton-Raphson scheme. Conventionally, the finite ele- ment methods （FEMs） or weak-form based meshfree methods have often been adopted to solve geometric nonlinear problems. However, issues, such as the mesh dependency, the numerical integration, and the boundary imposition, make these approaches com- putationally inefficient. Recently, strong-form collocation methods have been called on to solve the boundary value problems. The feasibility of the collocation method with the nodal discretization such as the radial basis collocation method （RBCM） motivates the present study. Due to the limited application to the nonlinear analysis in a strong form, we formulate the equation of equilibrium, along with the boundary conditions, in an incremental-iterative sense using the RBCM. The efficacy of the proposed framework is numerically demonstrated with the solution of two benchmark problems involving the geometric nonlinearity. Compared with the conventional weak-form formulation, the pro- posed framework is advantageous as no quadrature rule is needed in constructing the governing equation, and no mesh limitation exists with the deformed geometry in the increment al-it erative process.

点蚀损耗对船体梁极限强度的影响

The paper focuses on the assessment of the hull girder ultimate strength,combined with random pitting corrosion wastage,by the incremental-iterative method.After a brief review about the state of art,the local ultimate strength of pitted platings under uniaxial compression is preliminarily outlined and subsequently a closed-form design formula is endorsed in the Rule incremental-iterative method,to account for pitting corrosion wastage in the hull girder ultimate strength check.The ISSC bulk carrier is assumed as reference ship in a benchmark study,devoted to test the effectiveness of the incremental-iterative method,by a comparative analysis with a set of FE simulations,performed by Ansys Mechanical APDL.Four reference cases,with different locations of pitting corrosion wastage,are investigated focusing on nine combinations of pitting and corrosion intensity degrees.Finally,a comparative analysis between the hull girder ultimate strength,combined with pitting corrosion wastage,and the relevant values,complying with the Rule net scantling approach,is performed.Based on current results,the modified incremental-iterative method allows efficiently assessing the hull girder ultimate strength,combined with pitting corrosion wastage,so revealing useful both in the design process of new vessels and in the structural health monitoring of aged ships.