Newmark methods

Solutions for MDOF systems arc usually obtained through the use of finite element procedures. Due to nonlinearities associated with plasticity and possibly large displacements, the direct time integration method should be used. Various direct integration methods for time integration are employed but, the Newmark Method is perhaps he most common. Other methods, such as the Houboult Method, Wilson-T Method and the Central Difference Method are commonly used in finite element applications. Refer to Bathe 1995 for further details. 

This is an exact transcription of the formulas in Newmark s original paper, only substituting M p for the velocity v wherever it appears. In practice the choice a = 1/2 is used to avoid spurious damping (it can be demonstrated for a simple model problem) this certainly would appear to be desirable in the setting of molecular dynamics. For rj = 0 we then arrive at the Verlet method. For other values of r the scheme is clearly implicit, which likely is the reason it is rarely used in molecular simulation, although it is popular in structural mechanics. The implicit Newmark methods are not symplectic, but a related family of symplectic methods can be constructed by replacing interpolated forces by forces evaluated at interpolated positions [395]. 

The problem solved using implicit finite element procedure using Newmark method. Tensile stresses used for fractures extent identification. 

In the calculation, firstly, the value of yield seismic coefficient is calculated. Fundamentally, the procedure to calculate is based on the original Janbu method, while a modification was performed by considering the effects of earthquake inertia force and excess pore water pressure. Secondly, after the value has been obtained, the horizontal displacement is obtained following the procedure of Newmark method. Therefore, the procedure mentioned is an extended version of the combination of the Newmark and the Janbu methods (named as extended NJ method). 

The stmcture is loaded with forces caused by the horizontal North South component of the El Centro earthquake (Peknold Version). The commercial program Autodesk Robot Structural Analysis (2010) is used to solve the equations of motion with the help of the average acceleration version of the Newmark method. 

Figure 8.54 Diagram illustrating the Newmark method, a is the yield acceleration corresponding to FSpseudo-static = 1.0.

Courant condition when using an explicit time integration method (e.g., central difference method) for such small elements leads to small time increments and a huge computational cost. To resolve this problem, the Newmark-/ method (jS = 1/4, 5 = 1/2) is used for the time integration. Note that an explicit scheme is selected to compute the response robustly an implicit scheme sometimes does not reach an accurate solution because of complex nonlinear constitutive relation. Thus, to verify the convergence of a solution, attention must be paid to the spatial and temporal discretization. 

Eq. 4 at time t. Eor this reason the integration procedure is called an explicit integration method. On the other hand, the Houbolt, Wilson, and Newmark methods, considered in the next sections, use the equilibrium conditions at time t -I- At and are called implicit integration methods. 

Equation (149) is valid provided that the matrix T and that within the brackets are non-singular. It has been shown that this is always true in the case considered. (47) Since Newmark and Sederholm have used the exchange superoperator in its non-Hermitian form, such as that given in equation (117), their method is rather time-consuming. Probably, this is the reason why the method has been largely forgotten. 

G3. Green, R., Newmark, P. A., Musso, A. M., and Mollin, D, L., The use of chicken serum for measurement of serum vitamin B12 concentration by radioisotope dilution Description of method and comparison with microbiological assay results. Br. J. Haematol. 27, 507-527 (1974). 

Unsuccessful attempts to obtain this barbiturate derivative by the method of Helferich and Kosche have been reported (P. Newmark, PsTimidine Structure as Related to Chemical and Biological Activity, Ph. D. Thesis, Univ. of Colorado, 1952). 

Wargovich, M.J., Eng, V.W., and Newmark, H.L., Inhibition by plant phenols of benzo[a]pyrene-induced nuclear aberrations in mammahan intestinal cells a rapid in vivo assessment method. Food Chemical Toxicol Int. J. Br. Industrial Biological Res. Assoc., 23, 47 9,1985. 

An extensive review on intramolecular interactions of polyethers and polysulfides investigated by NMR has been written by Sasanuma. The author also discusses the application of vicinal couplings in conformational analysis of these compounds. Two-dimensional NMR methods of polymers have been reviewed by Newmark. ... 

As a special case of a partitioned Runge-Kutta method, consider the Newmark family of methods [280] defined for two parameters o and r] by the formulas... 

The simulations are carried out for the first 20 s of the first three, and the first 100 s of the last three earthquakes. The major response is seen in this time frame, and it also allows for more detail in the illustrations. A direct integration method for the solution of the equation of motion in Eq. 18.2 is used. Superposition of modal responses is not possible for systems with non-proportional damping, as is the case with the current structure with added dampers. The Newmark p method (by using the unconditionally stable average acceleration method) is used as the solver for aU simulations in this study. The function that implements this ordinary differential equation (ODE) solver makes sure that the simulation time step is 20 times smaller than the smallest period of the structure. If this is not the case, it interpolates the excitation data for a smaller time step, and later outputs the response at a 0.01 s. In this work, the building type structure has a minimum period of 0.108 s. Thus, the simulation takes place at 0.108/20 = 0.0054 s. 

The Newmark s p method (linear stiffness integration method) is also applied to take account of the non-linear part of the whole structure. If the linear stiffiiess is much larger than the non-linear stiffness, the integration method is unconditionally stable. In this work, the equations were transformed into an incremental form. It was confirmed that even when the incremental form of the equations is applied, the condition where the linear stiffness is larger than the non-linear tangent stiffness ensures that the integration method gives a stable solution. 

As a rational combination of Newmark s sliding block method (Newmark, 1965) and Janbu method (Janbu, 1957), extended Newmark and Janbu method (extended NJ method) has been used in earthquake induced slope failure (Deng etal.,2010). 

The extended Newmark and Janbu method (extended NJ method) can be used to calculate the velocity and displacement of slope due to increase in ground water level. In the calculation, the seismic acceleration was set to be zero. When the seismic yield acceleration reaches zero due to GWL increase, the sliding is triggered. The sliding is accelerated due to a negative K. At the end of the sliding, will recover to be positive. 

Miles, S.B. Ho, C.L. 1999. Rigorous landslide hazard zonation using Newmark s method and stochastic ground motion simulation. Soil Dynamics and Earthquake Engineering 18 305-323. 

The methods for analyzing seismic slope stability mainly include pseudostatic analysis (Terzhagi, 1950), stress-deformation analysis (Clough et al., 1966) and Newmark s permanent displacement analysis (Newmark, 1965). Miles Ho (1999), Wang Sassa (2007) obtained the critical earthquake peak acceleration of a slope by Nevraiark s permanent displacement method, then compared this acceleration with the anti-seismic precautionary earthquake peak acceleration to evaluate seismic stability of the slope, and finally used the exceeding probability of antiseismic precautionary earthquake peak acceleration to estimate the probability of earthquake-induced slope failures. So far, only the factor of seismic intensity has been taken into account in these methods, other seismic elements. 

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