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The Newmark-beta method is a method of numerical integration used to solve certain differential equations.It is widely used in numerical evaluation of the dynamic response of structures and solids such as in finite element analysis to model dynamic systems.
Settlement is the downward movement or the sinking of a structure's foundation. It is mostly caused by changes in the underlying soil, such as drying and shrinking, wetting and softening, or compression due to the soil being poorly compacted when construction started. [1] Some settlement is quite normal after construction has been completed.
Fills can also be used to cover tree stumps, rocks, or unstable soil, in which case material with a higher bearing capacity is placed on top of the obstacle in order to carry the weight of the roadway or railway and reduce differential settlement. [2]
The first modern theoretical models for soil consolidation were proposed in the 1920s by Terzaghi and Fillunger, according to two substantially different approaches. [1] The former was based on diffusion equations in eulerian notation, whereas the latter considered the local Newton’s law for both liquid and solid phases, in which main variables, such as partial pressure, porosity, local ...
Figure 1.Comparison of different schemes. In applied mathematics, the central differencing scheme is a finite difference method that optimizes the approximation for the differential operator in the central node of the considered patch and provides numerical solutions to differential equations. [1]
A building foundation or construction of a new embankment will cause the soil below to consolidate and this will cause settlement which in turn may cause distress to the building or embankment. Karl Terzaghi developed the theory of one-dimensional consolidation which enables prediction of the amount of settlement and the time required for the ...
In computational fluid dynamics, the MacCormack method (/məˈkɔːrmæk ˈmɛθəd/) is a widely used discretization scheme for the numerical solution of hyperbolic partial differential equations. This second-order finite difference method was introduced by Robert W. MacCormack in 1969. [1]
The slope deflection method is a structural analysis method for beams and frames introduced in 1914 by George A. Maney. [1] The slope deflection method was widely used for more than a decade until the moment distribution method was developed.