Development of quadrilateral spline thin plate elements using the B-net method

The quadrilateral discrete Kirchhoff thin plate bending element DKQ is based on the isoparametric element Q8, however, the accuracy of the isoparametric quadrilateral elements will drop significantly due to mesh distortions. In a previous work, we constructed an 8-node quadrilateral spline element L8 using the triangular area coordinates and the B- net method, which can be insensitive to mesh distortions and possess the second order completeness in the Cartesian co- ordinates. In this paper, a thin plate spline element is devel- oped based on the spline element L8 and the refined tech- nique. Numerical examples show that the present element indeed possesses higher accuracy than the DKQ element for distorted meshes.

Finite Element Calculation of the Flexural Stiffness of Corroded RC Eccentric Compressive Members

A finite element calculation model of corroded RC eccentric compressive members was build using finite element software ANSYS. The model considers the decline of mechanical properties and the effective section of a corroded steel bar,as well as the deterioration of bond character between corroded reinforcement and concrete. The reliability of the finite element model was evaluated by comparing the results of the finite element calculation with the data from experiments. Based on the finite element analysis results,the influence of corrosion degree,the diameter change of the longitudinal reinforcing bars and the spacing change of stirrups on the flexural stiffness were calculated and analyzed.

Study on spline wavelet finite-element method in multi-scale analysis for foundation

A new finite element method （FEM） of B-spline wavelet on the interval （BSWI） is proposed. Through analyzing the scaling functions of BSWI in one dimension, the basic formula for 2D FEM of BSWI is deduced. The 2D FEM of 7 nodes and 10 nodes are constructed based on the basic formula. Using these proposed elements, the multiscale numerical model for foundation subjected to harmonic periodic load, the foundation model excited by external and internal dynamic load are studied. The results show the pro- posed finite elements have higher precision than the tradi- tional elements with 4 nodes. The proposed finite elements can describe the propagation of stress waves well whenever the foundation model excited by extemal or intemal dynamic load. The proposed finite elements can be also used to con- nect the multi-scale elements. And the proposed finite elements also have high precision to make multi-scale analysis for structure.

Construction of n-sided polygonal spline element using area coordinates and B-net method

In general, triangular and quadrilateral elements are commonly applied in two-dimensional finite element methods. If they are used to compute polycrystalline materials, the cost of computation can be quite significant. Polygonal elements can do well in simulation of the materials behavior and provide greater flexibility for the meshing of complex geometries. Hence, the study on the polygonal element is a very useful and necessary part in the finite element method. In this paper, an n-sided polygonal element based on quadratic spline interpolant, denoted by PS2 element, is presented using the triangular area coordinates and the B-net method. The PS2 element is conforming and can exactly model the quadratic field. It is valid for both convex and non-convex polygonal element, and insensitive to mesh distortions. In addition, no mapping or coordinate transformation is required and thus no Jacobian matrix and its inverse are evaluated. Some appropriate examples are employed to evaluate the performance of the proposed element.

Two 8-node quadrilateral spline elements by B-net method

Isoparametric quadrilateral elements are widely used in the finite element method, but the accuracy of the isoparametric quadrilateral elements will drop obviously deteriorate due to mesh distortions. Spline functions have some properties of simplicity and conformality. Two 8-node quadrilateral elements have been developed using the trian- gular area coordinates and the B-net method, which can ex- actly model the quadratic field for both convex and concave quadrangles. Some appropriate examples are employed to evaluate the performance of the proposed elements. The nu- merical results show that the two spline elements can obtain solutions which are highly accurate and insensitive to mesh distortions.

THE CONSTRUCTION OF WAVELET-BASED TRUNCATED CONICAL SHELL ELEMENT USING B-SPLINE WAVELET ON THE INTERVAL

Based on B-spline wavelet on the interval （BSWI）, two classes of truncated conical shell elements were constructed to solve axisymmetric problems, i.e. BSWI thin truncated conical shell element and BSWI moderately thick truncated conical shell element with independent slopedeformation interpolation. In the construction of wavelet-based element, instead of traditional polynomial interpolation, the scaling functions of BSWI were employed to form the shape functions through the constructed elemental transformation matrix, and then construct BSWI element via the variational principle. Unlike the process of direct wavelets adding in the wavelet Galerkin method, the elemental displacement field represented by the coefficients of wavelets expansion was transformed into edges and internal modes via the constructed transformation matrix. BSWI element combines the accuracy of B-spline function approximation and various wavelet-based elements for structural analysis. Some static and dynamic numerical examples of conical shells were studied to demonstrate the present element with higher efficiency and precision than the traditional element.

Vibration Analysis of Beams by Spline Finite Element

In this paper,the spline finite element method is developed to investigate free vibration problems of beams.The cubic B-spline functions are used to construct the displacement field.The assembly of elements and the introduction of boundary conditions follow the standard finite element procedure.The results under various boundary conditions are compared with those obtained by the exact method and the finite difference method.It shows that the results are in excellent agreement with the analytical results and much more accurate than the results obtained by the finite difference method,especially for higher order modes.

The Calculation of Stress-Strain State of Anisotropic Composite Finite-Element Area with Different Boundary Conditions on the Surface

The numerical analytic research approach of stress-strain state of anisotropic composite finite element area with different boundary conditions on the surface, is represented below. The problem is solved by using a spatial model of the elasticity theory. Differential equation system in partial derivatives reduces to one-dimensional problem using spline collocation method in two coordinate directions. Boundary problem for the system of ordinary higher-order differential equation is solved by using the stable numerical technique of discrete orthogonalization.

A 3D pyramid spline element

In this paper,a 13-node pyramid spline element is derived by using the tetrahedron volume coordinates and the B-net method,which achieves the second order completeness in Cartesian coordinates.Some appropriate examples were employed to evaluate the performance of the proposed element.The numerical results show that the spline element has much better performance compared with the isoparametric serendipity element Q20 and its degenerate pyramid element P13 especially when mesh is distorted,and it is comparable to the Lagrange element Q27.It has been demonstrated that the spline finite element method is an efficient tool for developing high accuracy elements.

Numerical solution of Poisson equation with wavelet bases of Hermite cubic splines on the interval

A new wavelet-based finite element method is proposed for solving the Poisson equation. The wavelet bases of Hermite cubic splines on the interval are employed as the multi-scale interpolation basis in the finite element analysis. The lifting scheme of the wavelet-based finite element method is discussed in detail. For the orthogonal characteristics of the wavelet bases with respect to the given inner product, the corresponding multi-scale finite element equation can be decoupled across scales, totally or partially, and suited for nesting approximation. Numerical examples indicate that the proposed method has the higher efficiency and precision in solving the Poisson equation.

A cubic quadrilateral spline element with concave shapes

Basic requirement for applying isoparametric element is that the element has to be convex and no violent distortion is allowed. In this paper, a cubic quadrilateral spline element with 12 nodes has been developed using the triangular area coordinates and the B-net method, which can exactly model the cubic field for quadrilateral element with both convex and concave shapes. Neither mapping nor coordinate transformation is required and the spline element can obtain high accuracy solutions and insensitive to mesh distortions.

Collocation Method for Solving the Generalized KdV Equation

In this work, we have obtained numerical solutions of the generalized Korteweg-de Vries (GKdV) equation by using septic B-spline collocation finite element method. The suggested numerical algorithm is controlled by applying test problems including;single soliton wave. Our numerical algorithm, attributed to a Crank Nicolson approximation in time, is unconditionally stable. To control the performance of the newly applied method, the error norms, L2 and L∞ and invariants I1, I2 and I3 have been calculated. Our numerical results are compared with some of those available in the literature.

局部环向变厚度方钢管混凝土柱偏压力学性能研究

针对海洋环境中飞溅区造成的钢管混凝土柱局部环向腐蚀现象,采用机械削减方式模拟钢管壁厚局部环向腐蚀,进行了7个方钢管混凝土柱偏压试验,揭示了削弱率和偏心率对其偏压承载力的影响,并通过数值模拟对削弱率进行拓展分析.提出了基于削弱率的偏压承载力降低系数,代入中、美规范进行偏压承载力计算.结果表明:钢管的局部环向变厚度严重削弱了方钢管混凝土柱的偏压承载力和侧向挠曲能力;较大的加载偏心率也降低了其偏压承载力,但增大了其侧向挠曲能力.引入偏压承载力降低系数后,根据中、美规范计算得到的偏压承载力与试验值均吻合较好;相比于我国规范,美国规范在计算偏压承载力时相对更加保守.

高温作用后新型高强QN1803不锈钢轴压构件局部稳定性能研究

通过建立新型高强度QN1803不锈钢工字形和方矩形截面短柱的有限元模型对其高温作用后的局部稳定性能进行了数值模拟分析.通过参数分析探究了残余应力、局部初始几何缺陷及温度工况对构件局部稳定性能及极限承载力的影响.研究结果表明:对于方矩形构件及截面正则化长细比小于1.0的厚实工字形构件,残余应力对承载力的影响较小;对于薄柔工字形构件,残余应力会降低其截面承载力,且降低幅度随着温度的升高而下降.此外,随着温度升高,初始几何缺陷对不锈钢工字形构件承载力产生显著影响且正则化宽厚比的影响限值变大,对不锈钢方矩形构件承载力的影响则相反.最后,本文基于参数分析结果,评估了现行欧洲规范EN 1993-1-4、美国规范ASCE/SEI-8-02以及中国《不锈钢结构技术规程》(CECS 410:2015)中不锈钢构件局部稳定性能常温设计方法的适用性,发现了现有设计方法中对高强不锈钢轴心受压构件的高温作用后设计指导尚存在不合理之处并提出了优化建议.

二阶非线性抛物方程的B样条有限元法

首先,用二次B样条有限元法求解Fisher-Kolmogorov(FK)方程,证明半离散格式与全离散格式解的稳定性与收敛性;其次,用Crank-Nicolson方法离散时间变量,得到近似解的收敛阶为O((Δt)^(2)+h^(3));最后,用数值算例验证了理论分析结果及B样条有限元法的有效性.

Numerical Exploration of Asymmetrical Impact Dynamics: Unveiling Nonlinearities in Collision Problems and Resilience of Reinforced Concrete Structures

This study provides a comprehensive analysis of collision and impact problems’ numerical solutions, focusing ongeometric, contact, and material nonlinearities, all essential in solving large deformation problems during a collision.The initial discussion revolves around the stress and strain of large deformation during a collision, followedby explanations of the fundamental finite element solution method for addressing such issues. The hourglassmode’s control methods, such as single-point reduced integration and contact-collision algorithms are detailedand implemented within the finite element framework. The paper further investigates the dynamic responseand failure modes of Reinforced Concrete (RC) members under asymmetrical impact using a 3D discrete modelin ABAQUS that treats steel bars and concrete connections as bond slips. The model’s validity was confirmedthrough comparisons with the node-sharing algorithm and system energy relations. Experimental parameterswere varied, including the rigid hammer’s mass and initial velocity, concrete strength, and longitudinal and stirrupreinforcement ratios. Findings indicated that increased hammer mass and velocity escalated RC member damage,while increased reinforcement ratios improved impact resistance. Contrarily, increased concrete strength did notsignificantly reduce lateral displacement when considering strain rate effects. The study also explores materialnonlinearity, examining different materials’ responses to collision-induced forces and stresses, demonstratedthrough an elastic rod impact case study. The paper proposes a damage criterion based on the residual axialload-bearing capacity for assessing damage under the asymmetrical impact, showing a correlation betweendamage degree hammer mass and initial velocity. The results, validated through comparison with theoreticaland analytical solutions, verify the ABAQUS program’s accuracy and reliability in analyzing impact problems,offering valuable insights into collision and impact problems’ nonlinearities and practical strategies for enhancingRC structures’ resilience under dynamic stress.

二次B-Spline时域基函数的TDFEM的应用

提出了时域有限元法(TDFEM)的一种新的基函数—二次B-spline时域基函数.首先简述了时域有限元法的原理和基本公式;然后提出了新型的基于B-spline函数的条件稳定和无条件稳定的时域有限元法方案,并应用于三维电磁辐射问题.通过典型的算例对这两种方案的精度、运算时间进行了比较,证实了基于二次B-spline函数的时域有限元法的有效性.通过稳定性理论分析得出该算法的精确稳定性,并且通过数值计算的结果得到验证.

基于Coons曲面与B-spline曲线的有限元网格自动生成

在概述了有限元网格自动生成的基础上,介绍了一种能对复杂曲边区域作有限元网格生成的技术。这种技术以Coons曲面作映射函数,以B-spline曲线作拟合区域边界,充分发挥ICG的交互能力,利用B-spline曲线的形状控制,对多种复杂曲边区域作网格自动生成。用该技术研制的网格生成系统在交互式人机界面支持下,能快速输入几何信息,实现图形交互编辑,边界贴合良好,内部网格点理想。

Scanning Based Induction Heating for AISI 4340 Steel Spline Shafts-3D Simulation and Experimental Validation

This paper presents an investigation of non-stationary induction heating process applied to AISI 4340 steel spline shafts based on 3D simulation and experimental validation. The study is based on the knowledge, concerning the form of correlations between various induction heating parameters and the final hardness profile, developed in the case of stationary induction heating. The proposed approach focuses on analyzing the effects of variation of frequency, power and especially scanning speed through an extensive 3D finite element method simulation, comprehensive sensitivity study and structured experimental efforts. Based on coupled electromagnetic and thermal fields analysis, the developed 3D model is used to estimate the temperature distribution and the hardness profile. Experimentations conducted on a commercial dual-frequency induction machine for AISI 4340 steel splines confirm the feasibility and the validity of the proposed modelling procedure. The 3D model validation reveals a great concordance between simulated and measured results, confirms that the model can effectively be used as framework for understanding the process and for assessing the effects of various parameters on the hardening process quality and performance and consequently leads to the most relevant variables to use in an eventual hardness profile prediction model.

预制双钢板剪力墙围护结构热力学数值研究

预制双钢板组合剪力墙抗侧力性能表征良好,但由于内部高热导率组件繁多造成不均匀传热,易形成局部低温区域引发结露霉变.基于预制双钢板组合剪力墙围护结构的热力学性能优化,提出一类围护结构构造设计原型,利用COMSOL Multiphysics建立有限元计算模型,结合参数化方法,探究双钢板剪力墙的保温设计参数、结构组件参数对其墙体内部的热流分布影响规律.研究结果表明:保温锚栓形成的点状热桥远大于对拉螺栓,双层钢板塞焊连接处则未出现明显温度波动,相邻构造层中不同连接件应保持一定间距,使热流尽可能通过完整保温层,避免形成连续热桥.相较于无热桥时的理想模型,含连接件时实际模型单位面积的壁面法向总热通量显著增益;改用低热导率保温材料能够明显减少主体法向热通量,但对点状热桥的抑制作用有限,热通量减小梯度随材料热导率减小而增大,保温材料宜将防火性能佳、经济成本低的岩棉或热导率低的EPS作为技术经济性优选;增大板厚能够有效抑制点状热桥处法向热通量,且该作用随板厚增大而减小;连接件在能够达到结构要求时建议优先增大布置间距、减小锚固深度以改善内部温度分布,其次考虑改用低热导率的玻璃钢制连接件改善局部热流,最后在锚固末端加覆保温砂浆或隔热垫块有效削弱热桥的影响.研究得到了法向热通量分布关于保温设计、结构组件中热工相关参数的变化规律,以指导双钢板剪力墙结构体系的围护结构热工设计.