Yinghua Liu

Boundary element methods for lower bound limit and shakedown analysis

Abstract Limit and shakedown theorems are exact theories of classical plasticity for the direct computation of the load-carrying capacity under constant and varying loads. Based on Melans theorem, a solution procedure for limit and shakedown analysis is established making use of symmetric Galerkin boundary element method (SGBEM) for two-dimensional (2D) structures and traditional boundary element method (BEM) for three-dimensional (3D) structures. The self-equilibrium stress fields are expressed by linear combination of several basic self-equilibrium stress fields with parameters to be determined. These basic self-equilibrium stress fields are elastic responses of the body to impose permanent strains obtained through elastic–plastic incremental analysis by SGBEM for 2D structures and by BEM for 3D structures, respectively. The Complex method is used to solve resulting non-linear programming directly and determine the maximal load amplifier. The numerical results show that it is efficient and accurate to solve limit and shakedown analysis problems by using the BEM and the Complex method. In this paper, the limit analysis is treated as a special case of shakedown analysis in which only proportional loading is considered.

On the solution of limit load and reference stress of 3-D structures under multi-loading systems

The concepts of limit load and reference stress have been widely used in structural engineering design and component integrity assessment, especially considering multi-loading systems. The limit analysis of structures and the reference stress method (RSM) have been proven to be successful in problems pertaining to two-criteria failure assessment, creep growth, rupture damage, and more recently, elastic-plastic fracture toughness. However, the determination of limit load and reference stress of 3-D structures under multi-loading systems is not a simple task. In the present paper, a solution method for radial loading is presented, the mathematical programming formulation is derived for the upper bound limit analysis of 3-D structures under multi-loading systems, and moreover, a direct iterative algorithm used to determine the reference stress is proposed which depends on the evaluation of limit load. The penalty function method is used to deal with the plastic incompressibility condition. All the numerical examples show that the proposed radial loading path scheme is reasonable and effective. The mathematical programming method without search used here can overcome the difficulties caused by the nonlinearity and nonsmoothness of the objective function and avoid the complicated computations of incremental elastic-plastic analysis.

Low-Frequency Acoustic-Structure Analysis Using Coupled FEM-BEM Method

A numerical algorithm based on finite element method (FEM) and boundary element method (BEM) is proposed for the analyses of acoustic-structure coupled problems. By this algorithm, the structural domain and the acoustic domain are modelled by FEM and BEM, respectively, which are coupled with each other through the consideration of the appropriate compatibility and equilibrium conditions on the interface of the two domains. To improve the computational efficiency, the adaptive cross approximation (ACA) approach is incorporated into the proposed algorithm to deal with the nonsymmetric and fully populated matrices resulting from the coupling of the FEM and BEM. The validity and the high efficiency of the present approach are demonstrated by two examples.

Collapse load computation of defective pipelines under multi-loading system

Department of Engineering Mechanics, Tsinghua University, Beijing 100084, P.R. China Based on the kinematic theorem of limit analysis, a finite element mathematical programming formulation of 3-D rigid-perfectly plastic bodies is presented. The penalty function method is used to deal with the plastic incompressibility. A direct iterative algorithm is employed in solving the above formulation. The numerical procedure has been applied to carry out the limit analysis of pipelines with or without defects on the outside surface under multi-loading system. The effects of ellipsoidal and rectangular part-through slots on the collapse loads of pipelines under multi-loading system are investigated in detail. All the numerical ex-amples are given to illustrate its application.

The compression and friction of tubular rubber seal under the curved surface loading

In this paper, the mechanical behaviors of the tubular rubber seal under the curved surface loading are studied by the experimental and finite element methods. First, both the compressive behaviors and the frictional performance of the tubular rubber seal under the plane loading are studied experimentally. Second, two-dimensional finite element model about the tubular rubber seal is established and the constitutive model parameters of the rubber seal material are extracted. Finally, the mechanical behavior of the tubular rubber seal under the curved surface loading is investigated by means of the approximation analysis method and the finite element simulation. The results indicate that the physical parameters based on the experiment and finite element method simulation of the tubular rubber seal under the plane loading can describe the mechanical behavior under the curved surface loading. Both the strain distribution of the tubular rubber seal and the driving torque are slightly influenced by the friction coefficient between the tubular rubber seal and the curved surfaces. The influence factor of the friction coefficient on the driving torque is proposed, which plays an important role in the design and evaluation of advanced tubular rubber seal.

Recent developments of the linear matching method framework for structural integrity assessment

The LMM subroutines and plug-in tools for structural integrity assessment are now in extensive use in industries for the design and routine assessment of power plant components. This paper presents a detailed review and case study of the current state-of-the art LMM direct methods applied to the structural integrity assessment. The focus is on the development and use of the LMMF on a wide range of crucial aspects for the power industry. The LMMF is reviewed to show a wide range of capabilities of the direct methods under this framework, and the basic theory background is also presented. Different structural integrity aspects are covered including the calculation of shakedown, ratchet and creep rupture limits. Furthermore, the crack initiation assessments of an un-cracked body by the LMM are shown for cases both with and without the presence of a creep dwell during the cyclic loading history. Finally an overview of the in house developed LMM plug-in is given, presenting the intuitive Graphical User Interface developed. The efficiency and robustness of these direct methods in calculating the aforementioned quantities are confirmed through a numerical case study, which is a semi-circular notched (Bridgman notch) bar. A 2D axisymmetric finite element model is adopted, and the notched bar is subjected to both cyclic and constant axial mechanical loads. For the crack initiation assessment, different cyclic loading conditions are evaluated to demonstrate the impact of the different load types on the structural response. The impact of creep dwell is also investigated to show how this parameter is capable of causing in some cases a dangerous phenomenon known as creep ratcheting. All the results in the case study demonstrate the level of simplicity of the LMMs but at the same time accuracy, efficiency and robustness over the more complicated and inefficient incremental finite element analyses.

Mismatch Constraint Effect of Creep Crack With Modified Boundary Layer Model

Mismatch effect plays a crucial role in weldments, and an independent mismatch constraint parameter M* is proposed to characterize the material mismatch constraint effect in this paper. A mismatched modified boundary layer (MBL) model for creeping solids is developed to simulate the stress field of creep cracks in mismatched weldments. It can be found that there still exists the similarity between creep crack tip stress fields under different mismatch factors. Numerical results show that M* obtains the minimum value on the under match condition and the maximum value on the over match condition. Comparisons between M* and other geometric constraint parameters (A2(t) and Q22) are carried out and the applicability of M* is verified. A modified assessment formula for creep crack growth rate ratio is proposed based on the parameter M*. It is found that M* is a reasonable and remarkable parameter to characterize the mismatch constraint effect of creeping cracks.

Strength and Buoyancy Analyses of Floating Roof With Continuous Beams and Dome Frames Under Rainwater Loading

In this paper, the strength and buoyancy problems of the floating roof with continuous beams and dome frames are analyzed by the finite element method (FEM) and model experiment method. The modified-loading method with relationship between deflection and load is developed to carry out the FEM analysis of the floating roof under rainwater loading, and a model experiment is also configured to prove the reasonability of the numerical method and to assist the analysis. The deflections, strains, and sinking problems of the floating roof with continuous beams and dome frames are simulated by the present FEM and tested by the experiment, respectively. The floating roof without beams, ribs, or frames is also simulated by the present FEM. The numerical results are compared to the corresponding experimental ones. According to these results, the problems of strength and buoyancy of the floating roof with continuous beams and dome frames are also investigated and discussed. These results will provide some available references to designs and studies in the industry.

Prediction Model of Mechanical Extending Limits in Horizontal Drilling and Design Methods of Tubular Strings to Improve Limits

Mechanical extending limit in horizontal drilling means the maximum horizontal extending length of a horizontal well under certain ground and down-hole mechanical constraint conditions. Around this concept, the constrained optimization model of mechanical extending limits is built and simplified analytical results for pick-up and slack-off operations are deduced. The horizontal extending limits for kinds of tubular strings under different drilling parameters are calculated and drawn. To improve extending limits, an optimal design model of drill strings is built and applied to a case study. The results indicate that horizontal extending limits are underestimated a lot when the effects of friction force on critical helical buckling loads are neglected. Horizontal extending limits firstly increase and tend to stable values with vertical depths. Horizontal extending limits increase faster but finally become smaller with the increase of horizontal pushing forces for tubular strings of smaller modulus-weight ratio. Sliding slack-off is the main limit operation and high axial friction is the main constraint factor constraining horizontal extending limits. A sophisticated installation of multiple tubular strings can greatly inhibit helical buckling and increase horizontal extending limits. The optimal design model is called only once to obtain design results, which greatly increases the calculation efficiency.

Numerical investigations on the effects of T-stress in mode I creep crack

The effects of T-stress on the stress field, creep zone and constraint effect of the mode I crack tip in power-law creeping solids are presented based on finite element (FE) analysis in the paper. The characteristics of the crack tip field in power-law creep solids by considering low negative T-stress and high positive T-stress are studied in the paper. The differences of T-stress effect on the crack tip field between power-law creeping solids and elastoplastic materials are also clarified. A modified parameter is proposed to characterize the influence of T-stress on creep zone. The constraint parameter Q under both small-scale creep and large-scale creep with various T-stresses for the modified boundary layer (MBL) model and various specimens with different crack depths are given. The applicability and the limitation of the MBL model for creep crack are also investigated. The inherent connection between T-stress and Q-parameter is discussed. The investigations given in this paper can further promote the ...