A new implicit dynamic finite element analysis procedure with damping included

To analyze a multibody system, this paper proposes an implicit numerical integration method for joint coordinates subsystem synthesis method. To verify the proposed method, a multibody model for an unmanned robot vehicle, which consists of six identical independent suspension systems, is developed. The symbolic method is applied to compute the system Jacobian matrix for the implicit integration method. The proposed method is also verified by performing rough terrain run-over simulation in comparison with the conventional implicit integration method. In addition, to evaluate the efficiency of the proposed method, the CPU time obtained by using this method is compared with that obtained by using the conventional implicit method.

A class of nonlinear velocity-dependent problems must be solved iteratively for conventional integration methods since there exists no completely explicit integration method among them. A completely explicit structure-dependent integration method is developed in this work, and it can be applied to solve such problems non-iteratively. A completely explicit method for time integration is characterized by the adoption of explicit difference formulas for both the displacement and velocity increment. It can be derived from an eigen-based theory, and this theory can provide a fundamental basis for the feasibility of time integration. The new method generally has no serious disadvantages of weak instability and unusual overshoot in high-frequency steady-state responses that have been found in the current completely explicit structure-dependent integration methods. It is analytically and numerically verified that it can be used to solve nonlinear velocity-dependent problems without nonlinear iterations and can have a comparable accuracy in contrast to the solutions obtained from conventional integration methods with an iteration procedure. Its computational efficiency due to no nonlinear iterations is also affirmed by numerical examples.

This work exploits the recently developed telescopic projective numerical integration method for efficient parallel circuit simulation. Stable explicit numerical integration is achieved by adopting an explicit inner integrator (e.g. forward Euler) in a multi-level telescopic projective framework, thereby addressing the well-known stability limitation of many explicit numerical integration methods. In the presented approach, the effective time step of the entire multilevel integration is no longer limited by the smallest time constant of the circuit so as to safeguard stability. Rather, it is controlled solely by the accuracy requirement. This makes it possible to explore the natural parallelizability of such explicit integration method for parallel circuit simulation. We demonstrate the potential of the presented approach and its parallel implementation on multi-core machines with encouraging initial results.

Although many families of integration methods have been successfully developed with desired numerical properties, such as second order accuracy, unconditional stability and numerical dissipation, they are generally implicit methods. Thus, an iterative procedure is often involved for each time step in conducting time integration. Many computational efforts will be consumed by implicit methods when compared to explicit methods. In general, the structure-dependent integration methods (SDIMs) are very computationally efficient for solving a general structural dynamic problem. A new family of SDIM is proposed. It exhibits the desired numerical properties of second order accuracy, unconditional stability, explicit formulation and no overshoot. The numerical properties are controlled by a single free parameter. The proposed family method generally has no adverse disadvantage of unusual overshoot in high frequency transient responses that have been found in the currently available implicit integration methods, such as the WBZ-α method, HHT-α method and generalized-α method. Although this family method has unconditional stability for the linear elastic and stiffness softening systems, it becomes conditionally stable for stiffness hardening systems. This can be controlled by a stability amplification factor and its unconditional stability is successfully extended to stiffness hardening systems. The computational efficiency of the proposed method proves that engineers can do the accurate nonlinear analysis very quickly.

A satisfied cloth simulation should be general, accurate, efficient and stable. Explicit, implicit and semi-implicit integration methods have contributed to large performance enhancements in the field of cloth simulation. In this paper, we propose a modified embedded Runge-Kutta method to solve the cloth simulation based on classical spring-mass model. Traditional embedded Runge-Kutta methods generally apply some optimized coefficients to solve ordinary differential equations of cloth simulation. Most of them tend to concentrate on the efficiency of the simulation process, and not the fidelity of the simulation result. We investigate and determine the extent to which the overall quality must be compromised in order for the stable conditions to be satisfied. The modified Runge-Kutta method proposed in our paper incorporates the fixed time step and adaptive time step in solving cloth motion equations to achieve a controllable error evaluation. Compared with the other Runge-Kutta methods, the proposed method has some advantages for cloth simulation: controllable error evaluation without extra computations, excellent efficiency, good stability and satisfied precision. Experiment demonstrates that this method results in simulation efficiency improvements and is considerable practicable.

It it the purpose of this paper to review the results on the construction and implementation of diagonally implicit multistage integration methods for ordinary differential equations. The systematic approach to the construction of these methods with Runge---Kutta stability is described. The estimation of local discretization error for both explicit and implicit methods is discussed. The other implementations issues such as the construction of continuous extensions, stepsize and order changing strategy, and solving the systems of nonlinear equations which arise in implicit schemes are also addressed. The performance of experimental codes based on these methods is briefly discussed and compared with codes from Matlab ordinary differential equation (ODE) suite. The recent work on general linear methods with inherent Runge---Kutta stability is also briefly discussed

In this investigation, a non-incremental solution procedure for the finite rotationand large deformation analysis of plates is presented. The method, whichis based on the absolute nodal coordinate formulation, leads to plateelements capable of representing exact rigid body motion. In thismethod, continuity conditions on all the displacement gradients areimposed. Therefore, non-smoothness of the plate mid-surface at the nodalpoints is avoided. Unlike other existing finite element formulationsthat lead to a highly nonlinear inertial forces for three-dimensionalelements, the proposed formulation leads to a constant mass matrix, andas a result, the centrifugal and Coriolis inertia forces are identicallyequal to zero. Furthermore, the method relaxes some of the assumptionsused in the classical and Mindlin plate models and automatically satisfiesthe objectivity requirements. By using a generalcontinuum mechanics approach, a relatively simple expression for theelastic forces is obtained. Generalization of the formulation to thecase of shell elements is discussed. As examples of the implementationof the proposed method, two different plate elements are presented; oneplate element does not guarantee the continuity of the displacementgradients between the nodal points, while the other plate elementguarantees this continuity. Numerical results are presented in order todemonstrate the use of the proposed method in the large rotation anddeformation analysis of plates and shells. The numerical results, whichare compared with the results obtained using existing incrementalprocedures, show that the solution obtained using the proposed methodsatisfies the principle of work and energy. These results are obtainedusing explicit numerical integration method. Potential applications ofthe proposed method include high-speed metal forming, vehiclecrashworthiness, rotor blades, and tires.

A delayed treatment effect is a commonly observed phenomenon in tumor immunotherapy clinical trials. It can cause a loss of statistical power and complicate the interpretation of the analytical findings. This phenomenon also poses challenges for interim analysis in the context of phase II/III seamless design or group sequential design. It shows potential to lead researchers to make incorrect go/no-go decisions. Despite its significance, rare research has explored the impact of delayed treatment effects on the decision success rate of the interim analysis and the methods to compensate for this loss. In this study, we propose an analysis procedure based on change points for improving the decision success rate at the interim analysis in the presence of delayed treatment effects. This procedure primarily involves three steps: I. detecting and testing the number and locations of change points; II. estimating treatment efficacy; and III. making go/no-go decisions. Simulation results demonstrate that when there is a delayed treatment effect with a single change point, using the proposed analysis procedure significantly improves the decision success rate while controlling the type I error rate. Moreover, the proposed method exhibits very little disparity compared to the unadjusted method when the proportional hazards assumption holds. Therefore, the proposed analysis procedure provides a feasible approach for decision-making at the interim analysis when delayed treatment effects are present.

A comparison of the static and dynamic short-circuit calculation procedures has shown that the dynamic procedure, with enhanced machine modeling, produces results which agree well with national standards and minimizes the engineering design effort, with only a small increase in computational overhead. Time overcurrent relay settings and tripping times obtained by a dynamic short-circuit calculation are compared with fault clearing times obtained by modeling the relays using a traditional step-by-step dynamic analysis procedure. These two very different methods of calculation yield results which are in close agreement, reaffirming the validity of the dynamic short-circuit calculation procedure and offering evidence that the practice of basing the setting of time overcurrent relays on fault currents relating to time t=500 ms is well founded. The authors also demonstrate how inclusion of protection setting and transient modeling facilities in power system CAD (computer-aided design) packages offers the opportunity to include automatically and reliably the effect of the protection in any subsequent transient studies of the system. The main benefit is that this can highlight omissions or sensitivities in the protection arrangements.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

In this collaborative research project between Pennsylvania State University, Colorado State University and Florida State University, we mainly focused on developing multi-resolution algorithms which are suitable to regional ocean modeling. We developed hybrid implicit and explicit adaptive multirate time integration method to solve systems of time-dependent equations that present two signi cantly di erent scales. We studied the e ects of spatial simplicial meshes on the stability and the conditioning of fully discrete approximations. We also studies adaptive nite element method (AFEM) based upon the Centroidal Voronoi Tessellation (CVT) and superconvergent gradient recovery. Some of these techniques are now being used by geoscientists(such as those at LANL).

A novel decoupling dynamic method with third-order accuracy and controllable dissipation

SummaryTo improve the computational efficiency of the numerical manifold method for discontinuous deformation simulations, a spatial‐domain coupled explicit‐implicit time integration algorithm is proposed. A subdomain partition algorithm based on a super manifold element is developed for the numerical manifold method to simulate dynamic motions of blocky rock mass. In different subdomains, explicit or implicit time integration method is employed respectively based on its contact and motion status. These subdomains interact through assembling the corresponding explicit or implicit time integration‐based matrices of different rock blocks. The computational efficiency of the discontinuity system under dynamic loading is improved by partially diagonalizing the global matrices. Two verification examples of a sliding block along an inclined plane under a horizontal acceleration excitation and a multiblock system acted on by dynamic forces are studied to examine the accuracy of the proposed numerical method, respectively. A highly fractured rock mass situated on an inclined slope subjected to seismic excitations is then studied to show the computational efficiency of the developed algorithm. The simulated results are in good agreement with those from the versions using purely implicit or explicit time integration algorithm for the numerical manifold method. The computational efficiency is shown to be higher using the proposed algorithm, which demonstrates its potential for application in dynamic analysis of highly fractured rock masses.

A GPU-based numerical manifold method for modeling the formation of the excavation damaged zone in deep rock tunnels

Mixed implicit–explicit (IMEX) schemes combine elements of both implicit and explicit time integration methods. This allows to efficiently handle boundary value problems with severe differences in stiffness, such as often encountered in soil dynamics. A spatially mixed IMEX scheme, in which different parts of the computational domain may be treated implicitly or explicitly depending on their behaviour, is discussed in this work. Domain decomposition by means of a mortar contact discretisation is used for this purpose and multiple systems of equations are solved. The merits of the scheme in solving problems of soil dynamics are demonstrated, for which the governing equations are extended to hydro-mechanical coupling.

Prediction of chatter stability for milling process using precise integration method