Study On Stochastic 2-D Crack Propagation Problem With Isogeometry Boundary Element Method

The numerical simulation of crack propagation for engineering structures plays a guiding role in modern industrial design.However,uncertainties are ubiquitous in actual engineering,and it may be caused by a series of reasons,such as: inherent material randomness,geometric dimensions,manufacturing deviations,and dynamic loading.Comprehensive consideration of the influence of actual random parameters on the structural system can improve the reliability of the evaluation.This paper conducts the stochastic analysis of the crack propagation problem and investigates the influence of some important parameters on the structural response.The isogeometric boundary element method(IGABEM)is used to simulate the deterministic fracture problem.The core idea of the IGABEM is to use the spline basis function of the geometric model constructed in computer aided design(CAD)as the interpolation shape function used to approximate the geometric and the physical field of the structure in computer aided engineering(CAE)analysis.The most important advantage of IGABEM is that it can directly use the CAD model for numerical calculations,without the need for meshing after model design and re-meshing during the crack propagation simulation process,while maintaining geometric accuracy.Furthermore,the crack surface and propagation path can be parameterized explicitly.It is a highly automated,high-precision numerical calculation method.In addition,the boundary element method has the advantages of boundary representation,semi-analytical,etc.,which can calculate crack problems more conveniently and accurately.In this paper,a thermoelastic analysis method based on the IGABEM is established,and a crack propagation simulation scheme based on the IGABEM is used to numerically simulate and analyze the hydraulic fracturing under complex conditions.In addition,a stochastic analysis framework for linear elastic fracture problems is constructed to quantitatively analyze the random fracture problems.This work enhances the applicability of the crack propagation algorithm based on the isogeometric boundary element method for complex problems.The main content and innovations of the paper are as follows:(1)The IGABEM is applied to the thermoelasticity problem.Due to the existence of thermal stress,a domain integral term appears in the boundary integral equation,which violates the boundary representation property of the boundary element method.In this paper,we introduced the radial integration method into IGABEM and transformed the domain integration into boundary integration,thus solving this problem.This method not only maintains the advantages of the boundary element method in dimensionality reduction,but also realizes the seamless integration of CAD and CAE.(2)The IGABEM is used to simulate the hydraulic fractures under constant pressure.The Non-Uniform Rational B-splines(NURBS)are used to construct the crack curve,which can effectively characterize the crack surface and propagation path.By inserting graded knot near the crack tip,the stress singularity at the crack tip can be effectively captured.The M integral method is used to extract the stress intensity factors(SIFs)and compared with experiments and other numerical methods to verify the correctness of the algorithm in this paper.Moreover,we investigate the influence of different factors,including the confining pressure,crack numbers,pore pressure,and natural cracks,on hydraulic fractures and study how multiple cracks propagate under various conditions.(3)Construct a stochastic analysis framework for linear elastic fracture problems.Monte Carlo simulation(MCs)is adopted to address the multi-dimensional uncertainties,whose computation cost is reduced by combination of proper orthogonal decomposition(POD)and the radial basis function(RBF).MCs can effectively solve complex problems,but at the cost of a large amount of calculation,and the POD reduced-order model can alleviate this problem.Unlike the traditional algorithm,the present scheme can approximate the design subspace with radial basis function,thereby achieving the compressed expression of system information and effectively reducing the computation cost.