In this article, the stability of bars subjected to compressible loads at multi points on its axis is investigated, the system of equilibrium equations in buckling configuration is derived, its general solution is given, and, finally, the nonlinear equation for critical load is obtained that is the generalization of Euler’s formula.
Based on the characteristics of the restrained finite element equilibrium equations in the analysisof the initial and bifurcate post-buckling behavior, the paper gives out a valuable method to change itto be non-restrained equations, and then the numerical example.
This thesis studies three groups of application equations dealing with configuration of equilibrium of spatial force series, which is applied to engineering, It puts forward transpositive conditions between the basic form of equilibrium equations and the three groups of application equation, and proves them, which a(?) ms at extending the application of equations of configuration of equilibrium of spatial force series.
The isolation effect of cracks on domain of influence for a Gauss point is dealt by visibility criterion. Contributive equation of reciprocity between the two faces of the cracks to the system of equilibrium equations is derived.
Stress component functions are used to solve the problems of elasticity based on the equilibrium equations and stress compatible equation according to boundary conditions.
For the static analysis of 3D framed structures, the calculations of displacements and internal forces of static structures was first attributed to the determination of a carry-over and distribution matrix and a source vectors resulting from the equilibrium equations and compatibility conditions for displacements of each joint.
This method uses the free torsional theory and the principle of virtual work to build governing equilibrium equations involving unknown shear flows and twisting rate.
There have been obtained system of equilibrium equations and recurrence relations for its coefficients which enable us to formulate the algorithm to build the system.
The level populations were determined by numerically solving the equation of recombination kinetics together with the statistical equilibrium equations for a 60-level model hydrogen atom.
Certain difficulty arises when it is necessary to analyze elastic stability of thin-walled curved open tubes subjected to concentrated forces and moments and constrained by rather complicated boundary conditions. In this paper, starting with the equilibrium equations of curved open tube and using the method of fictitious distributing loading, we have obtained a system of ordinary differential equations with variable coefficients which can be used to calculate critical loads of structures. ...
In this paper, we based on reference[l] .improved and extended that which it is concerned to investigate the finite deflection equations of anisotropic laminated shallow shells subjected to static loads.dynamic loads and thermal loads. We have considered the most general bending-stretcbing couplings and the shear deformations in the thickness direction, and derived the equilibrium equations, boundary conditions and initial conditions. The differential equations expressed in terms of ...
Following the form given by Reissner in 1950 for elastic analysis, a general variational functional in plasticity is prescribed as∏in eq. (1). By setting its first variation o∏due to the variation of (σij,ui) to zero, the Euler equations derived in (3) are proved to be the equilibrium equations, a deformation type of stress-strain relations and boundary conditions for the prebuckling fundamental path solution. As Kappus had done in 1939, a new variation δ* can be imposed on (δσij,δui). Let...