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991.
Yu. N. Shevchenko R. G. Terekhov N. N. Tormakhov 《International Applied Mechanics》2007,43(3):291-302
Energy-coupled stress and strain measures are defined in Euler coordinates. They are used to analyze the relationship between
the first invariants of the stress and strain tensors for linearity and to determine strains at which the plastic component
of the first strain invariant can be neglected. It is established that this relationship remains linear within an engineering
plastic-strain tolerance of 0.2% irrespective of the value of strain intensity, which depends on the type of material and
its stress state
__________
Translated from Prikladnaya Mekhanika, Vol. 43, No. 3, pp. 60–72, March 2007. 相似文献
992.
Two definitions of free energy for a linear viscoelastic material, due to Graffi and to Coleman and Owen, are considered, and the compatibility of these definitions with some expressions of the free energy proposed in the literature is examined. For the expressions of Staverman and Schwarzl and of Breuer and Onat, the two definitions are proved to be equivalent, and the set of all relaxation functions for which the two expressions are indeed free energies is determined. Two more expressions, proposed by Volterra and Graffi and by Morro and Vianello, are taken into consideration. For them, only the classes of relaxation functions for which they are free energies according to the first definition, is completely characterized. All results are established under regularity assumptions weaker than those usually made in the literature. 相似文献
993.
This paper establishes spatial estimates in a prismatic (semi-infinite) cylinder occupied by an anisotropic homogeneous linear elastic material, whose elasticity tensor is strongly elliptic. The cylinder is maintained in equilibrium under zero body force, zero displacement on the lateral boundary and pointwise specified displacement over the base. The other plane end is subject to zero displacement (when the cylinder is finite, say). The limiting case of a semi-infinite cylinder is also considered and zero displacement on the remote end (at large distance) is not assumed in this case. A first approach is developed by considering two mean-square cross-sectional measures of the displacement vector whose spatial evolution with respect to the axial variable is studied by means of a technique based on a second-order differential inequality. Conditions on the elastic constants are derived that show the cross-sectional measures exhibit alternative behaviour and in particular for the semi-infinite cylinder that there is either at least exponential growth or at most exponential decay. A second approach considers cross-sectional integrals involving the displacement and its gradient and furnishes information upon the spatial evolution, without restricting the range of strongly elliptic elastic constants. Such models are principally based upon a first-order differential inequality as well as on one of second order. The general results are explicitly presented for transversely isotropic materials and graphically illustrated for a cortical bone. 相似文献
994.
The Stroh formalism is employed to discuss the existence of transient surface waves on a viscoelastic anisotropic hall-space. The compatibility conditions, obtained using the integral formulation of Lothe and Barnett [13, 14], are examined on the basis of an asymptotic expansion of the viscoelastic kernel and a separation of space variables. Some previous results on elastic media are extended to viscoelasticity, exploiting the consequences of the second law of thermodynamics. It is found that all the allowed transient surface modes take the form of inhomogeneous plane waves whose amplitude exponentially decays along the propagation direction on the surface. Special solutions are derived explicitly for one-component surface waves where transient modes are admitted also in those cases in which stationary waves cannot occur.
Mathematics Subject Classifications (2000) 74D05, 74J15. 相似文献
995.
The controllability for switched linear system with time-delay in controls was first investigated. The whole work contains
three parts. This is the first part, including problem formulation and some preliminaries. Firstly, the mathematical model
of switched linear systems with time-delay in control functions was presented. Secondly, the concept of column space, cyclic
invariant subspace and generalized cyclic invariant subspace were introduced. And some basic properties, such as separation
lemma, were presented. Finally, a basic lemma was given to reveal the relation between the solution set of a centain integral
equations and the generalized cyclic invariant subspace. This lemma will play an important role in the determination of controllability.
All these definitions and lemmas are necessary research tools for controllability analysis.
Contributed by YE Qing-kai
Foundation items: the National Natural Science Foundation of China (69925307, 60274001); the National Key Basic Reasearch and Development
Program (2002CB312200); the Postdoctoral Program Foundation of China
Biography: XIE Guang-ming (1972∼), Doctor (E-mail: xiegming@mech.pku.edu.cn) 相似文献
996.
On the use of stretched-exponential functions for both linear viscoelastic creep and stress relaxation 总被引:1,自引:0,他引:1
The use of the stretched-exponential function to represent both the relaxation function g(t)=(G(t)-G ∞)/(G 0-G ∞) and the retardation function r(t) = (J ∞+t/η-J(t))/(J ∞-J 0) of linear viscoelasticity for a given material is investigated. That is, if g(t) is given by exp (?(t/τ)β), can r(t) be represented as exp (?(t/λ)µ) for a linear viscoelastic fluid or solid? Here J(t) is the creep compliance, G(t) is the shear modulus, η is the viscosity (η?1 is finite for a fluid and zero for a solid), G ∞ is the equilibrium modulus G e for a solid or zero for a fluid, J ∞ is 1/G e for a solid or the steady-state recoverable compliance for a fluid, G 0= 1/J 0 is the instantaneous modulus, and t is the time. It is concluded that g(t) and r(t) cannot both exactly by stretched-exponential functions for a given material. Nevertheless, it is found that both g(t) and r(t) can be approximately represented by stretched-exponential functions for the special case of a fluid with exponents β=µ in the range 0.5 to 0.6, with the correspondence being very close with β=µ=0.5 and λ=2τ. Otherwise, the functions g(t) and r(t) differ, with the deviation being marked for solids. The possible application of a stretched-exponential to represent r(t) for a critical gel is discussed. 相似文献
997.
一种低精度惯性测量单元的精确标定技术 总被引:1,自引:3,他引:1
低精度惯性测量单元的温度特性和非线性严重,为补偿光纤陀螺的温度特性和非线性,通过高低温、多速率的标定实验研究了光纤陀螺输出电压与温度、转速的关系,采用零偏和标度因数统一标定的思想提出了光纤陀螺分段模型;为补偿MEMS加速度计的温度特^陛,通过高低温位置实验研究了加速度计输出电压与温度、输入加速度的关系,提出了加速度计分段模型。采用逐步线性回归对以上模型进行了简化。实时补偿效果表明,当温度从-30℃到60℃变化时,在±60(°)/s转速内角速度误差基本小于0.02(°)/s,加速度误差小于0.005g. 相似文献
998.
Jeremiah G. Murphy 《Journal of Elasticity》2007,86(2):139-154
The form of the classical stress–strain relations of linear elasticity are considered here within the context of nonlinear
elasticity. For both Cauchy and symmetric Piola-Kirchhoff stresses, conditions are obtained for the associated strain fields
so that they are independent of the material constants and compatible with existence of a strain–energy function. These conditions
can be integrated in both cases to obtain the most general strain field that satisfies these conditions and the corresponding
strain–energy function is obtained. In both cases, a natural choice of form of solution is suggested by the special case of
the compatibility conditions being satisfied identically. It will be shown that some strain–energy functions previously introduced
in the literature are special cases of the results obtained here. Some recent linear stress–strain relations, proposed in
the context of Cauchy elasticity, are examined to see if they are compatible with hyperelasticity.
相似文献
999.
D. N. Mikhailov 《Fluid Dynamics》2006,41(1):112-120
The problem of the propagation of longitudinal Biot waves in a porous medium saturated with a weakly compressible liquid (water) or a gas is considered theoretically. The frequency dependence of the phase velocities and damping coefficients is investigated numerically. It is shown that for a certain relationship between the parameters of the porous medium and the saturating fluid there is a “critical” frequency at which the properties of longitudinal waves of both kinds are identical. An analytical expression for this “critical” frequency is obtained. It is shown that for a gas-saturated porous medium, at a certain frequency, in both longitudinal waves the relative gas-matrix motion changes type. Assuming that the saturating-gas behavior corresponds to an adiabatic equation of state, an estimate is obtained for the threshold pore pressure necessary for the restructuring of the relative motion. The wave associated with matrix deformation is shown to have a high damping coefficient in a porous medium saturated with a weakly compressible liquid (water in the case considered) but to be only weakly damped in a gas-saturated porous medium. 相似文献
1000.
The purpose of this research is to further investigate the effects of material inhomogeneity on the decay of Saint-Venant
end effects in linear isotropic elasticity. This is carried out within the context of anti-plane shear deformations of an
inhomogeneous isotropic elastic solid. The mathematical issues involve the effects of spatial inhomogeneity on the decay rates
of solutions to Dirichlet or Neumann boundary-value problems for a second-order linear elliptic partial differential equation
with variable coefficients on a semi-infinite strip. In previous work [1], the elastic coefficients were assumed to be smooth
functions of the transverse coordinate so that the material was inhomogeneous in the lateral direction only. Here we develop
a new technique, based on a change of variable, to study generally inhomogeneous isotropic materials. The governing partial
differential equation is transformed to a Helmholtz equation with a variable coefficient, which facilitates analysis of the
influence of material inhomogeneity on the diffusion of end effects. For certain classes of inhomogeneous materials, an explicit
optimal decay estimate is established. The results of this paper are applicable to continuously inhomogeneous materials and,
in particular, to functionally graded materials.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献