Under the condition that all the perfectly plastic stress components ata crack tip are the functions of θ only, making use of the Tresca yieldcondition and equilibrium equations, we derive the generally analyticalexpressions of the perfectly plastic stress field at a plane-stress crack tip.
According to the point of view that the influence of groundwater on rock slopes stability is related to the porosity of rockmasses and the density groundwater, this paper has derived linear elasto-static equilibrium equations considering seepage field.
1. Verify the feasibility to adopt cellular automata to solid mechanics analysis. And based on the equilibrium equations, geometrical equations and constitutive equations cellular automata that may be used to solve 2-D truss elastic problems, 2-D truss plastic problems, 2-D rigid framework elastic problems and 2-D continuum elastic problems are introduced or presented.
Simplifying the three global limit equilibrium equations (horizontal force equilibrium equation, vertical force equilibrium equation and moment equilibrium equation) for potential slip mass by the assumed normal force of slice base, a cubical algebraic equation is derived in terms of safety factor Fs, of which the significant root is the explicit solution to safety factor Fs for general slice method which rigorously satisfies the global equilibrium conditions for potential slip mass.
By simplifying the three global limit equilibrium equations(horizontal force equilibrium equation,vertical force equilibrium equation and moment equilibrium equation) for potential slide mass by the assumed normal force of slice base,a linear equation of the acceleration factor is derived,the root of which is the explicit solution of the acceleration factor for general slice method and rigorously satisfies the global equilibrium conditions for potential slide mass.
The model solutions satisfy all the equilibrium equations, continuity and most of the boundary conditions, so they can be used to analyze the micromechanics and to evaluate the precision of fiber pullout models.
A nonlinear earth pressure distribution solution is proposed under the condition of multi-linear sliding surface, which is derived through the equilibrium equations of elements and by slice method, and it is also compared with the result from Coulomb’s earth pressure theory.
The equilibrium equations of the annular pla te under coudition of q(r) and q(r) sinnθ loads are established, and an Euler e quation expressed by deflection is developed.
According to equilibrium equations,geometric equations and constitutive equations,theoretical derivation of identifiability of back analysis was done when slope is in elastic state.
In order to research dynamic behavior of the cable-nets strctures, the dynamic equilibrium equations and relevant mechanics matrixs are conduted according to Hamilton theory.
The non-linear differential equations are acquired by using power functions as trial functions and through the collocation method when the results of equilibrium equations are sought.
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.
In this paper, the foundation bed is taken as a semielastic body and elastic theory is used to derive the settlement equations for any point on the superficies when vertical uniform load is applied to a rectangular area c×b on the superficies. The ring foundation is divided into several parts equal in length. According to the deformation compatibility equations at the ends of each part and the statical equilibrium equations of the parts, the general equations of the ring founda...
Based on the shell theory, arch dam, in general, may be approximately considered as being composed of three fundamental systems of structures, such as cantilever beams, horizontal arches and torsional structures. During analysing them in this manner, treating the cantilever beams as the beams on elastic foundation offered by the horizontal arches is preferable. Taking both radial or torsional actions into accout, equilibrium equations for bearing points on cantilever beams are established throug...
This paper is a follow-up of paper[1] , in which approximate integral method is used to give a numerical solution of two dimensional problems (the Maxwell model) . In this paper, two- and three-dimensional problems are concerned, where two generalized functions E and S have been introduced, the displacement, stress and pore pressure etc. are determined to satisfy the fundamental equilibrium equations and Darcy's law respectively, thus the calculation is simplified.By means of Laplace transformat...