Research On Meshless Method And Its Application In Cathodic Protection Problems

Cathodic protection(CP)plays an important role in protecting offshore structures from corrosion.More and more numerical simulations are employed in designing and evaluating cathodic protection systems with the development of computers and numerical methods.The CP problem is governed by Laplace's equation,and mostly simulated by boundary element method(BEM).However,BEM consumes a large amount of computer memory and is very inefficient when it is used to simulate large-scale models.The element-free methods are rather mature with decades' development and have been successfully applied in many engineering problems such as fluid dynamics,heat conduction and elasticity.Most of the meshless methods are more accurate than the conventional methods such as finite element method and BEM.Boundary node method(BNM)and boundary face method(BFM)are boundary type meshless methods.They are based on boundary integral equation just like BEM.Thus the model of BNM and BFM can also be easily built.As BNM and BFM are more accurate than BEM,they can achieve the same precision with less nodes and thus less computer memory.The objective of this thesis is to research the theory of meshless methods,and develop boundary type meshless methods and a software for the cathodic protection problems of marine structures.The following work is conducted to achieve this objective.Approximation methods such as moving least square(MLS)method and moving Kriging interpolation(MKI)method are researched.A complex variable MKI(CVMKI)method is proposed to improve the efficiency of MKI.CVMKI can be used in both 2D boundary type and domain type meshless methods.Numerical examples show that CVMKI can achieve higher accuracy and efficiency.A stabilized MKI(SMKI)is proposed with shifted and scaled polynomial basis to improve the accuracy and stability of MKI.Both CVMKI and MKI are integrated in the software to simulate cathodic protection problems.The BFM is developed to simulate the CP problem,and an integration scheme is developed for triangles with curved edges.Two common potential problems are solved to validate the accuracy.The results show that BFM is more accurate than BEM.Then,the CP problems of a subsea pipeline,an hourglass type floating production storage and offloading system(FPSO)and a tension-leg platform(TLP)are simulated.The results show that BFM is more accurate than BEM and costs less time when the same precision is achieved in most cases.A simulation software is developed based on the above work,thus the work of this research can be easily used to solve engineering problems.The visualization module is developed with C#and OpenG and can display 3D mesh model,geometry model and contour nephogram.It can also translate,rotate,scale the view of 3D models,and select the triangles and surfaces on the models.The geometry software module is developed based on non-uniform rational B-splines(NURBS),and can import geometry model from CAD/CAE softwares via IGES file.The meshing software module for BFM is developed based on transfinite interpolation method and advancing front technique,and is validated by many meshing cases.The computing module is developed based on BFM and the theory of cathodic protection problems,and can be used easily and efficiently to simulate the CP problems of marine structures.