STOCHASTIC BOUNDARY ELEMENT METHOD FOR RELIABILITY ANALYSIS OF PLATE AND BEAMS COMPOSITE STRUCTURES

In this paper, the reliability of orthotropic plate and beams composite structures, which is under the actions of the stochastic loading and stochastic boundary conditions, have been analyzed by stochastic boundary element method. First, the boundary integral equation of orthotropic plate and beams composite structures is given in this paper, and then based on the stochastic boundary element method, the method for reliability analysis of stochastic structures is establishes and formulas for computation of reliability index of orthotropic plate and beams composite structures are obtained. The computed examples show the efficient of the method used in this paper.

THE STOCHASTIC BOUNDARY ELEMENT METHOD IN STATISTICAL ANALYSIS OF MODERATELY THICK PLATES

In this paper a stochastic boundary element method (SEEM) is developed to analyze moderately thick plates with random material parameters and random thickness. Based on the Taylor series expansion, the boundary integration equations concerning the mean and deviation of the generalized displacements are derived, respectively. It is found that the randomness of material parameters is equivalent to a random load, so the mean and covariance matrices of unknown generalized boundary displacements and tractions can be obtained. Furthermore, the mean and covariance of generalized displacements and forces at internal points can also be obtained. A numerical example has been worked out with the method proposed and necessary analysis is made for the results.

Novel boundary element method for resolving plate bending problems

This paper discusses the application of the boundary contour method fo r resolving plate bending problems. The exploitation of the integrand divergence free property of the plate bending boundary integral equation based on the Kirc hhoff hypothesis and a very useful application of Stokes' Theorem are presented to convert surface integrals on boundary elements to the computation of bending potential functions on the discretized boundary points,even for curved surface elements of arbitrary shape. Singularity and treatment of the discontinued corne r point are not needed at all. The evaluation of the physics variant at internal points is also shown in this article. Numerical results are presented for some plate bending problems and compared against analytical and previous solutions.

The Boundary Element Method for Ordinary State-Based Peridynamics

The peridynamics(PD),as a promising nonlocal continuum mechanics theory,shines in solving discontinuous problems.Up to now,various numerical methods,such as the peridynamic mesh-free particlemethod(PD-MPM),peridynamic finite element method(PD-FEM),and peridynamic boundary element method(PD-BEM),have been proposed.PD-BEM,in particular,outperforms other methods by eliminating spurious boundary softening,efficiently handling infinite problems,and ensuring high computational accuracy.However,the existing PD-BEM is constructed exclusively for bond-based peridynamics(BBPD)with fixed Poisson’s ratio,limiting its applicability to crack propagation problems and scenarios involving infinite or semi-infinite problems.In this paper,we address these limitations by introducing the boundary element method(BEM)for ordinary state-based peridynamics(OSPD-BEM).Additionally,we present a crack propagationmodel embeddedwithin the framework ofOSPD-BEM to simulate crack propagations.To validate the effectiveness of OSPD-BEM,we conduct four numerical examples:deformation under uniaxial loading,crack initiation in a double-notched specimen,wedge-splitting test,and threepoint bending test.The results demonstrate the accuracy and efficiency of OSPD-BEM,highlighting its capability to successfully eliminate spurious boundary softening phenomena under varying Poisson’s ratios.Moreover,OSPDBEMsignificantly reduces computational time and exhibits greater consistencywith experimental results compared to PD-MPM.

FRACTURE CALCULATION OF BENDING PLATES BY BOUNDARY COLLOCATION METHOD

Fracture of Kirchhoff plates is analyzed by the theory of complex variables and boundary collocation method. The deflections, moments and shearing forces of the plates are assumed to be the functions of complex variables. The functions can satisfy a series of basic equations and governing conditions, such as the equilibrium equations in the domain, the boundary conditions on the crack surfaces and stress singularity at the crack tips. Thus, it is only necessary to consider the boundary conditions on the external boundaries of the plate, which can be approximately satisfied by the collocation method and least square technique. Different boundary conditions and loading cases of the cracked plates are analyzed and calculated. Compared to other methods, the numerical examples show that the present method has many advantages such as good accuracy and less computer time. This is an effective semi_analytical and semi_numerical method.

Monte Carlo Simulation of Fractures Using Isogeometric Boundary Element Methods Based on POD-RBF

This paper presents a novel framework for stochastic analysis of 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).In order to avoid re-meshing and retain the geometric exactness,isogeometric boundary element method(IGABEM)is employed for simulation,in which the Non-Uniform Rational B-splines(NURBS)are employed for representing the crack surfaces and discretizing dual boundary integral equations.The stress intensity factors(SIFs)are extracted by M integral method.The numerical examples simulate several cracked structures with various uncertain parameters such as load effects,materials,geometric dimensions,and the results are verified by comparison with the analytical solutions.

CALCULATION FOR PATH-DOMAIN INDEPENDENT J INTEGRAL WITH ELASTO-VISCOPLASTIC CONSISTENT TANGENT OPERATOR CONCEPT-BASED BOUNDARY ELEMENT METHODS

This paper presents an elasto-viscoplastic consistent tangent operator (CTO) based boundary element formulation, and application for calculation of path-domain independentJ integrals (extension of the classicalJ integrals) in nonlinear crack analysis. When viscoplastic deformation happens, the effective stresses around the crack tip in the nonlinear region is allowed to exceed the loading surface, and the pure plastic theory is not suitable for this situation. The concept of consistency employed in the solution of increment viscoplastic problem, plays a crucial role in preserving the quadratic rate asymptotic convergence of iteractive schemes based on Newton's method. Therefore, this paper investigates the viscoplastic crack problem, and presents an implicit viscoplastic algorithm using the CTO concept in a boundary element framework for path-domain independentJ integrals. Applications are presented with two numerical examples for viscoplastic crack problems andJ integrals.

DAMAGE ANALYSIS BY BOUNDARY ELEMENT METHOD

The response of cracked bodies subjected to loading was investigated by the boundary element method in this paper. The two-law elastic-cohesive-softening model was used for crack propagation analysis. The interface conditions for uncracked, craze, open crack, adhesive crack and slid crack parts were discussed and the corresponding incremental iteration algorithm was given. A simplified damage propagation model was presented. The technique has been applied to some specific examples which give the evidence that the method is satisfactory and efficient.

ELECTRO-MECHANICAL COUPLING ANALYSIS OF MEMS STRUCTURES BY BOUNDARY ELEMENT METHOD

In this paper,we present the applications of Boundary Element Method(BEM) to simulate the electro-mechanical coupling responses of Micro-Electro-Mechanical systems(MEMS). The algorithm is programmed in our research group based on BEM modeling for electrostatics and elastostatics.Good agreement is shown while the simulation results of the pull-in voltages are compared with the theoretical/experimental ones for some examples.

Numerical Crack Analysis of Blunt Rock Indenters by an Indirect Boundary Element Method

Linear elastic fracture mechanics principles are widely applied for the analysis of crack problems in rock fracture mechanics. Rock indentation is an important and complicated problem among rock engineering issues. In this paper, in addition to the fracture criterion of maximum tangential stress adjacent to crack tip, the higher order displacement discontinuity method (which is a version of the indirect boundary element method) has been used for modeling the crack propagation mechanism under blunt indenters. In order to achieve more accurate results, higher order boundary elements i.e. quadratic elements, has been used to calculate displacement discontinuities and also to reduce the singularities of stress and displacement fields near the crack tip, the special crack tip elements has been used to calculate the stress intensity factors (SIF) at the crack tips. In this modeling, the effect of crack angle on stress intensity factors has been investigated. The numerical results of stress intensity factors obtained from some example problems were compared to the theoretical and experimental results cited in the literature which always show a percentage error less than one percent. The simulated results may pave the way for increasing the efficiency of mining and drilling by improving the design of tools and indentation equipments.

EQUIVALENT BOUNDARY INTEGRAL EQUATIONS WITH INDIRECT UNKNOWNS FOR THIN ELASTIC PLATE BENDING THEORY

Equivalent Boundary Integral Equations (EBIE) with indirect unknowns for thin elastic plate bending theory, which is equivalent to the original boundary value problem, is established rigorously by mathematical technique of non-analytic continuation and is fully proved by means of the variational principle. The previous three kinds of boundary integral equations with indirect unknowns are discussed thoroughly and it is shown that all previous results are not EBIE.

SPECIAL HIGH-ORDER BENDING CRACK TIP FINITE ELEMENT FOR THE REISSNER PLATE

Based on the crack tip field expansion of the Reissner plate, a special high order bending crack tip element is developed, and the element stiffness matrix is given in the explicit form, which is especially convenient for engineering analyses. A numerical example is presented and compared with previous results to demonstrate the efficiency and accuracy of the special element.

Finite element simulation of elastoplastic fieldnear crack tips and results for a central crackedplate of le-lhp material under tension

The elastoplastic field near crack tips is investigated through finite element simulation.A refined mesh model near the crack tip is proposed. In the mesh refining area, element size continuously varies from the nanometer scale to themicrometer scale and the millimeter scale. Graphics of the plastic zone, the crack tip blunting, and the deformed crack tip elements are given in the paper.Based on the curves of stress and plastic strain, closely near the crack tip, the stresssingularity index and the stress intensity factor,as well as the plastic strain singularity index and the plastic strain intensity factor are determined.Thestress and plastic strainsingular index vary with the load, while the dimensions of the stress and the plastic strain intensity factorsdependon the stress and the plastic strain singularity index, respectively. The singular field near the elastoplastic crack tip is characterized by the stress singularity index and the stress intensity factor, or alternativelythe plastic strain singularity index and the plastic strain intensityfactor.At the end of the paper, following Irwin’s concept of fracture mechanics,σδKσδKcriterion andεδQεδQcriterion are proposed.Besides, crack tip angle criterion is also presented.

Transmitted and Reflected Coefficients for Horizontal or Vertical Plate Type Breakwater

Surface or submerged horizontal or vertical plate can be considered as a new concept breakwater. This paper investigates the wave-plate interaction of this type of breakwater by use of the boundary element method. The relationships of wave transmitted and reflected among plate thickness, submergence and length are carefully studied by numerical simulation. It is shown that： （1） The transmitted coefficients of submerged horizontal plate or vertical plate will become larger with the increase of plate thickness and reduce rapidly with the decrease of plate submergence. （2） Both surface horizontal and vertical plate are efficient for intermediate and short wave elimination, but vertical plate is more effective. （3） Submerged horizontal plate can act more effectively than submerged vertical plate does. With all wave frequencies, the vertical plate almost has no wave elimination effect.

Study on Scattering Wave Force of Horizontal and Vertical Plate Type Breakwaters

The interaction between wave and horizontal and vertical plates is investigated by the boundary element method, and the relations of wave exciting force with plate thickness, submergence and length are obtained. It is found that： 1） The efficient wave exciting force exists while plate submergence is less than 0.5 m, and the plate is very thin with order O（0.005 m）. 2） The maximum heave wave exciting force exists, and it is the main factor for surface and submerged horizontal plate while the roll force can be ignored. 3） The maximum sway wave exciting force exists, it is the main factor for surface or submerged vertical plate, and the roll force is about 20 times of horizontal plate.

Study on Hydrodynamic Coefficients of Double Submerged Inclined Plates

Added mass and damping coefficients are very important in hydrodynamic analysis of naval structures. In this paper,a double submerged inclined plates with ‘/\’ configuration is firstly considered. By use of the boundary element method(BEM) based on Green function with the wave term, the radiation problem of this special type structure is investigated. The added mass and damping coefficients due to different plate lengths and inclined angles are obtained. The results show that: the added mass and damping coefficients for sway are the largest. Heave is the most sensitive mode to inclined angles. The wave frequencies of the maximal added mass and damping coefficients for sway and roll are the same.

Flow Field Analysis of Submerged Horizontal Plate Type Breakwater

Submerged horizontal plate can be considered as a new concept breakwater. In order to reveal the wave elimination mechanism of this type breakwater, boundary element method is utilized to investigate the velocity field around plate carefully. The flow field analysis shows that the interaction between incident wave and reverse flow caused by submerged plate will lead to the formation of wave elimination area around both sides of the plate. The velocity magnitude of flow field has been reduced and this is the main reason of wave elimination.

Fracture mechanism of inclusions in thick plate center under tensile loading

Segregation of solute atoms in the center of thick plates of the tempered steel can cause an inhomogeneous structural transformation and generate micron-sized inclusions,which leads to lamellar tearing of thick plate and decreases the plasticity and toughness.The formation and fragmentation mechanisms of micron-sized inclusions,like MnS and(Nb,Ti)C,in the center of thick plates were investigated by using thermodynamic calculations,finite element simulations,and electron backscatter diffraction characterization techniques.The results show that micron-sized inclusions nucleate and grow in the liquid phase,and under tensile loading,they exhibit three fragmentation mechanisms.The local stress during the fragmentation of inclusions is lower than the critical fracture stress of adjacent grains,and phase boundaries can effectively impede crack propagation into the matrix.The existence of a low proportion of high-angle grain boundaries(58.1%)and high Kernel average misorientation value(0.534°)in the segregation band promotes inclusions fragmentation and crack propagation.The difference in crack initiation and propagation direction caused by the morphology of inclusions and physical properties,as well as different matrix arrest abilities,is the main reasons for the diversity of inclusion fragmentation.

A New Approximate Fundamental Solution for Orthotropic Plate

A weight double trigonometric series is presented as an approximate fundamental solution for orthotropic plate.Integral equation of orthotropic plate bending is solved by a new method, which only needs one basic boundary integral Eq., puts one fictitious boundary outside plate domain. Examples show that the approximate fundamental solution and solving method proposed in this paper are simple, reliable and quite precise. And they are applicable for various boundary conditions.

Study on Submerged Upper Arc-Shaped Plate Type Breakwater

Based on the wave radiation and diffraction theory, this paper investigates a new type breakwater with upper arcshaped plate by using the boundary element method(BEM). By comparing with other three designs of plate type breakwater(lower arc-shaped plate, single horizontal plate and double horizontal plate), this new type breakwater has been proved more effective. The wave exiting force, transmission and reflection coefficients are analyzed and discussed. In order to reveal the wave elimination mechanism of this type of breakwater, the velocity field around the breakwater is obtained. It is shown that:(1) The sway exciting force is minimal.(2) When the ratio of the submergence and wave amplitude is 0.05, the wave elimination effect will increase by 50% compared with other three types of breakwater.(3) The obvious backflow is found above the plate in the velocity field analysis.