## Advances in applied mathematics and mechanics in China. 1Applied mathematics and mechanics have been widely developed in China during the past twenty years. Especially in the development of generalized variational principles, finite deformation, singular perturbation theory, nonhomogenious elasticity, Chinese scientist have made a great impact by evolving new methods and concepts. This survey of the present situation in the area of science is a remarkable contribution to the academic exchange between China and other countries. It contains articles of the leading Chinese scientists in their respective fields. |

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### Contents

Nonlinear finite element method with mixed use | 25 |

The representation of isotropic linear asymmetric | 36 |

A new simplified approach to boundary integral | 49 |

Copyright | |

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amplitude bending boundary conditions boundary layer buckling Cauchy problem Chinese clamped coefficients complementary energy constant constraints cooling tower corrugated annular plate cos(n,x deflection determined displacement distribution edge eigenvalue eigenvector electrodes elementary solution equilibrium finite element method flow fluid frequency function given Hartmann number homogeneous homopolar device hyperbolic cooling tower incremental isotropic Kaiyuan Lanzhou University Lemma linear Liu Renhuai load mass flux mixed finite element mode mode shapes n n n non-homogeneity and variable NON-NEWTONIAN FLUIDS nonisotropic nonlinear numerical stability obtain parameter PDLV plane Poiseuille flow potential energy precision arithmetic region resonant triad respectively satisfy shallow shell shear shown in Fig simply supported solve stability stiffness matrix subregion generalized variational subregion mixed finite Substituting surface tensor Theorem tion V-typical column variable thickness variational principles vector velocity vortices x y xy Yeh Kaiyuan