基于弹性形变模型的自适应曲面细分建模

依据物体的几何特性来对曲面进行建模的细分算法近年来取得了卓越的发展并广泛应用于三维物体建模和动画制作,同时一些学者为了弥补基于几何的(geometry-based)细分建模方法在直观性上的不足,提出了基于物理的(physics-based)细分建模方法,这些方法大部分是采用有限元的技术结合传统的细分模式来实现的。虽然有限元技术适用于建立多种的物理模型,但是对于一些相对简单的弹性形变处理,其在计算复杂性及模型简洁性方面还可以针对具体的应用作一定的完善。本文针对材料力学中简单的可恢复弹性形变,使用柱状块体压缩拉伸模型(ICBCM)与自适应细分算法相结合的技术,在保证建模效果的基础上显著的减低了模型的复杂程度,并提高了细分算法的执行效率。

Nonlinear elastic deformation of magnesium and cobalt by Preisach-Mayergoyz model

A classic hysteretic model, Preisach-Mayergoyz model （P-M model）, was used to calculate the nonlinear elastic deformation of magnesium （Mg） and cobalt （Co）. Mg and Co samples in cylinder shape were compressively tested by uniaxial test machine to obtain their stress—strain curves with hysteretic loops. The hysteretic loops do have two properties of P-M hysteretic systems： wiping out and congruency. It is proved that P-M model is applicable for the analysis of these two metals’ hysteresis. This model was applied on Mg at room temperature and Co at 300 ℃. By the P-M model, Co and Mg nonlinear elastic deformation can be calculated based on the stress history. The simulated stress—strain curves agree well with the experimental results. Therefore, the mechanical hysteresis of these two metals can be easily predicted by the classic P-M hysteretic model.

A model of deformation of thin-wall surface parts during milling machining process

A three-dimensional finite element model was established for the milling of thin-walled parts. The physical model of the milling of the part was established using the AdvantEdge FEM software as the platform. The aluminum alloy impeller was designated as the object to be processed and the boundary conditions which met the actual machining were set. Through the solution, the physical quantities such as the three-way cutting force, the tool temperature, and the tool stress were obtained, and the calculation of the elastic deformation of the thin-walled blade of the free-form surface at the contact points between the tool and the workpiece was realized. The elastic deformation law of the thin-walled blade was then predicted. The results show that the maximum deviation between the predicted value and the actual measured machining value of the elastic deformation was 26.055 μm; the minimum deviation was 2.011 μm, with the average deviation being 10.154 μm. This shows that the prediction is in close agreement with the actual result.

Elastoplastic model for discontinuous shear deformation of deep rock mass

Deep rock mass possesses some unusual properties due to high earth stress,which further result in new problems that have not been well understood and explained up to date.In order to investigate the deformation mechanism,the complete deformation process of deep rock mass,with a great emphasis on local shear deformation stage,was analyzed in detail.The quasi continuous shear deformation of the deep rock mass is described by a combination of smooth functions:the averaged distribution of the original deformation field,and the local discontinuities along the slip lines.Hence,an elasto-plastic model is established for the shear deformation process,in which the rotational displacement is taken into account as well as the translational component.Numerical analysis method was developed for case study.Deformation process of a tunnel under high earth stress was investigated for verification.

Slope analysis based on local strength reduction method and variable-modulus elasto-plastic model

Employing an ideal elasto-plastic model,the typically used strength reduction method reduced the strength of all soil elements of a slope.Therefore,this method was called the global strength reduction method(GSRM).However,the deformation field obtained by GSRM could not reflect the real deformation of a slope when the slope became unstable.For most slopes,failure occurs once the strength of some regional soil is sufficiently weakened; thus,the local strength reduction method(LSRM)was proposed to analyze slope stability.In contrast with GSRM,LSRM only reduces the strength of local soil,while the strength of other soil remains unchanged.Therefore,deformation by LSRM is more reasonable than that by GSRM.In addition,the accuracy of the slope's deformation depends on the constitutive model to a large degree,and the variable-modulus elasto-plastic model was thus adopted.This constitutive model was an improvement of the Duncan–Chang model,which modified soil's deformation modulus according to stress level,and it thus better reflected the plastic feature of soil.Most importantly,the parameters of the variable-modulus elasto-plastic model could be determined through in-situ tests,and parameters determination by plate loading test and pressuremeter test were introduced.Therefore,it is easy to put this model into practice.Finally,LSRM and the variable-modulus elasto-plastic model were used to analyze Egongdai ancient landslide.Safety factor,deformation field,and optimal reinforcement measures for Egongdai ancient landslide were obtained based on the proposed method.

Influence of Tacking Sequence on Residual Stress and Distortion of Single Sided Fillet Submerged Arc Welded Joint

Submerged arc welding （SAW） is advantageous for joining high thickness materials in large structure due to high material deposition rate. The non-uniform heating and cooling generates the thermal stresses and subsequently the residual stresses and distortion. The longitudinal and transverse residual stresses and angular distortion are generally measured in large panel structure of submerged arc welded fillet joints. Hence, the objective of this present work is to quantify the amount of residual stress and distortion in and around the weld joint due to positioning of stiffeners tack. The tacking sequence influences the level of residual stress and proper controlling of tacking sequences is required to minimize the stress. In present study, an elasto-plastic material behavior is considered to develop the thermo mechanical model which predicts the residual stress and angular distortion with varying tacking sequences. The simulated result reveals that the tacking sequence heavily influences the residual stress and deformation pattern of the single sided fillet joint. The finite element based numerical model is calibrated by comparing the experimental data from published literature. Henceforth, the angular distortions are measured from an in-house developed experimental set-up. A fair agreement between the predicted and experimental results indicates the robustness of the developed numerical model. However, the most significant conclusion from present study states that tack weld position should be placed opposite to the fillet weld side to minimize the residual stress.

ELASTIC DEFORMATION ANALYSIS OF MULTILA YERED STRANDS

This paper describes a general model for the mechanical behavior studying of general wire rope strand. An exact solution of the deformation characteristics was given when the strands is under tensile and torsional loads. The theoretical results are useful in evaluating the extensional and torsional moduli of rigidity for the strands. Finally, a simple design criterion is establised for the nonrotating ropes.

Modeling of strength and deformation of overconsolidated clays based on bounding surface plasticity

An elastoplastic constitutive model for overconsolidated clays is established in the framework of the critical state theory and bounding surface plasticity theory. The bounding surface is defined as the maximum yield surface in the loading history. A yielding ratio, i.e., an internal variant, is defined as the size ratio of the current yield surface to the corresponding bounding surface. The yielding ratio instead of the overconsolidation ratio(OCR) is used to evaluate the strength and stress-strain behaviors of overconsolidated clays in the shearing process. The bounding stress ratio incorporating the effect of the yielding ratio is used to characterize the potential failure strength of the overconsolidated clays. The dilation stress ratio taking into account the effect of the yielding ratio is applied to describe the dilatancy behaviors of the overconsolidated clays. Comparisons between model predictions and test data show that the proposed model could well capture the strength and stress-strain behaviors of normally consolidated and overconsolidated clays.

Three dimensional efficient meshfree simulation of large deformation failure evolution in soil medium

An efficient Galerkin meshfree formulation for three dimensional simulation of large deformation failure evolution in soils is presented. This formulation utilizes the stabilized conforming nodal integration, where for the purpose of stability and efficiency a Lagrangian smoothing strain at nodal point is constructed and thereafter the internal energy is evaluated nodally. This formulation ensures the linear exactness, efficiency and spatial stability in a unified manner and it makes the conventional Galerkin meshfree method affordable for three dimensional simulation. The three dimensional implementation of stabilized conforming nodal integration is discussed in details. To model the failure evolution in soil medium a coupled elasto-plastic damage model is used and an objective stress integration algorithm in combination of elasto-damage predictor and plastic corrector method is employed for stress update. Two typical numerical examples are shown to demonstrate the effectiveness of the present method for modeling large deformation soil failure.

A new constitutive law for the nonlinear normal deformation of rock joints under normal load

In view of the deviation of the fitting results of the classical exponential model and the hyperbolic model （the BB model） from several experiment data during intermediate stress period, a new constitutive model for the nonlinear normal deformation of rock joints under normal monotonous load is established with flexibility-deformation method. First of all, basic laws of the deformation of joints under normal monotonous load are discussed, based on which three basic conditions which the complete constitutive equation for rock joints under normal load should meet are put forward. The analysis of the modified normal con- stitutive model on stress-deformation curve shows that the general exponential model and the improved hyperbolic model are not complete in math theory. Flexibility-deformation monotone decreasing curve lying between flexibility-deformation curve of the classical exponential model and the BB model is chosen, which meets basic conditions of normal deformation mentioned before, then a new normal deformation constitutive model of rock joints containing three parameters is established. Two main forms of flexibility-deformation curve are analyzed and specific math formulas of the two forms are deduced. Then the range of the parameters in the g-δ model and the g-2 model and the correlative influence factor in geology are preliminarily discussed. Referring to different experiment data, the validating analysis of the g-δ model and the g-γ model shows that the g-2 model can be applied to both the mated joints and unmated joints. Besides, experiment data can be better fit with the g-2 model with respect to the BB model, the classical exponential model and the logarithm model.

A relative permeability model for deformable soils and its impact on coupled unsaturated flow and elasto-plastic deformation processes.

Relative permeability is an indispensable property for characterizing the unsaturated flow and induced deformation in soils. The widely used Mualem model is inadequate for deformable soils because of its assumption of a rigid pore structure and the resultant unique dependence of the tortuosity factor on the volumetric water content. In this study, a unified relationship between the relative permeability and the effective degree of saturation was proposed for deformable soils by incorporating our newly developed water retention curve model into the original Mualem model, in which a new tortuosity factor was defined using the fractal dimension of flow paths and the mean radius of water-filled pores for representing the effect of pore structure variation. The modified deformation-dependent relative permeability model was verified using test data on five types of soils; the verification revealed a much better performance of the proposed model than the original model, which commonly overestimates the relative permeability of deformable soils. Finally, the proposed model was implemented in a coupled numerical model for examining the unsaturated flow and elastoplastic deformation processes in a soil slope induced by rain infiltration. The numerical results showed that the deformation-dependent nature of relative permeability has a remarkable effect on the elastoplastic deformation in the slope and that neglect of the deformation-dependent behavior of relative permeability causes overestimation of the depth of failure.

A curved surface solar radiation pressure force model for solar sail deformation

A precise force model is of vital importance for dynamics and control of solar sails. Among various factors, deviations from the ideal flat sails, elastic deformations of the sails, are really important as most solar sails are large flexible membranes. In this study, the deformed sails are modeled as smooth curved surfaces and a general total force model (GTFM) for the deformed sails is proposed. Various simplified versions of this GTFM are also derived for the symmetric deformation cases. Furthermore, differences between the ideal force models and our precise GTFM are investigated. The numerical results demonstrate that both the previous ideal reflected model and flat optical model are not as satisfactory as claimed before, by contrast with the actual dynamics from the GTFM. Thus this work paves the way for sail craft's precise navigation where exact forces are needed.