以基面力为状态变量,表征物体的受力状态;以其对偶量位移梯度表征物体的变形状态,介绍了一种新型的基于余能原理的有限变形问题有限元法─基面力元法(Base Force Element Method,BFEM)及其计算性能。该方法的特色是:(1)以基面力矢量为...
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以基面力为状态变量,表征物体的受力状态;以其对偶量位移梯度表征物体的变形状态,介绍了一种新型的基于余能原理的有限变形问题有限元法─基面力元法(Base Force Element Method,BFEM)及其计算性能。该方法的特色是:(1)以基面力矢量为基本未知量;(2)采用并矢运算推导基面力元法的张量表达式;(3)不用引入单元插值函数;(4)模型列式为积分显式,无需进行数值积分;(5)基面力元法列式将平面任意多边形单元、空间任意多面体单元集于一体;(6)可适用于任意坐标系。本文数值算例通过与平面4节点等参元(Q4模型)和平面4节点减缩积分单元(Q4R模型)的对比分析,考查基面力元法的计算性能,结果表明:基于余能原理的基面力元法对网格畸变和单元长宽比的影响不敏感,可以应用于高度几何非线性问题,可进行大荷载步计算,且计算精度较高、收敛性较好,具有较广阔的应用前景。
Quadrature element formulation for material nonlinear analysis of composite beams with partial interaction is derived on the basis of the Newmark kinematical model. The quadrature element method is characterized by di...
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Quadrature element formulation for material nonlinear analysis of composite beams with partial interaction is derived on the basis of the Newmark kinematical model. The quadrature element method is characterized by direct evaluation of the integrals involved in the variational description of a problem. The number of integration points in a quadrature element is adjustable in accordance with convergence requirement. A representative case is studied and results are compared with finite element solutions. It is shown that high computational accuracy and efficiency are achieved using the quadrature element method.
In this paper, wave propagations in jointed rock bars are investigated by the discontinuous deformation analysis (DDA) method. A way for the selection of the numerical control parameters in the DDA modeling is present...
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In this paper, wave propagations in jointed rock bars are investigated by the discontinuous deformation analysis (DDA) method. A way for the selection of the numerical control parameters in the DDA modeling is presented. Through the DDA modeling examples, the attenuation of stress waves propagating in a jointed rock mass characterized by both decreasing the amplitude and filtering the high frequency components are well manifested. Besides the joint stiffness and loading frequency, the joint strength and the incident angle may also influence in the propagations of the stress waves remarkably.
In mathematics, splines are piecewise polynomials satisfying certain continuity conditions. The shape functions can be treated as splines. It has been demonstrated that the spline method is an efficient tool for devel...
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In mathematics, splines are piecewise polynomials satisfying certain continuity conditions. The shape functions can be treated as splines. It has been demonstrated that the spline method is an efficient tool for developing effective elements. In this paper, we represent two conforming quadrilateral thin plate elements by the triangular area coordinates and B-net method.
The generalized composite rectangle (constant) rule for the computation of Cauchy principle value integral with kernel 1/(x-s) is discussed, and the asymptotic expansion of error function is obtained. Based on the asy...
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The generalized composite rectangle (constant) rule for the computation of Cauchy principle value integral with kernel 1/(x-s) is discussed, and the asymptotic expansion of error function is obtained. Based on the asymptotic expansion, a series is constructed to approach the singular point. An extrapolation algorithm is presented and the convergence rate is proved. At last, some examples are also illustrated to confirm the theoretical results and show the efficiency of the algorithms.
The pFFT algorithm is applied to accelerate the hybrid-domain BEM for acoustic problems. Based on the previous successful application of the pFFT algorithm to the exterior or interior domain BEM for acoustic problems,...
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The pFFT algorithm is applied to accelerate the hybrid-domain BEM for acoustic problems. Based on the previous successful application of the pFFT algorithm to the exterior or interior domain BEM for acoustic problems, the implementation of this algorithm in the hybrid-domain BEM for acoustic problems is studied in detail. To validate the software, simulation on a Helmholtz resonator is carried out and the results are compared with the corresponding ones by the direct BEM and analytical solution of the resonance frequency. As expected, the present results agree well with those by the direct BEM. But the remaining problem is that the GMRES solver without a preconditioner converges very slowly.
The Complex-variable differentiation method (CVDM) is a very promising method to compute derivatives of complicated functions and is free from cancellation errors which often occur in the finite difference method. In ...
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The Complex-variable differentiation method (CVDM) is a very promising method to compute derivatives of complicated functions and is free from cancellation errors which often occur in the finite difference method. In this paper, CVDM is developed for the two-variable situation and is first applied to isogeometric analysis method in which the computation of derivatives of rational functions represented by Non-Uniform Rational B-Splines (NURBS) method is very complicated. An example about h-refinement is given and the computational results show that CVDM in isogeometric analysis is correct and much simpler than using the traditional NURBS derivative formula.
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