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The purpose of this study, which is designed for the implementation of models in the implicit finite element framework, is to propose a robust, stable and efficient explicit integration algorithm for rate-independent elasto-plastic constitutive models.

The proposed automatic substepping algorithm is founded on an explicit integration scheme. The estimation of the maximal subincrement size is based on the stability analysis.

In contrast to other explicit substepping schemes, the algorithm is self-correcting by definition and generates no cumulative drift. Although the integration proceeds with maximal possible subincrements, high level of accuracy is attained. Algorithmic tangent stiffness is calculated in explicit form and optionally no analytical second-order derivatives are needed.

The algorithm is convenient for elasto-plastic constitutive models, described with an algebraic constraint and a set of differential equations. This covers a large family of materials in the field of metal plasticity, damage mechanics, etc. However, it cannot be directly used for a general material model, because the presented algorithm is convenient for solving a set of equations of a particular type.

The estimation of the maximal stable subincrement size is computationally cheap. All expressions in the algorithm are in explicit form, thus the implementation is simple and straightforward. The overall performance of the approach (i.e. accuracy, time consumption) is fully comparable with a default (built-in) ABAQUS/Standard algorithm.

The estimated maximal subincrement size enables the algorithm to be stable by definition. Subincrements are much larger than those in conventional substepping algorithms. No error control, error correction or local iterations are required even in the case of large increments.

Semi-implicit type cutting plane method (CPM) and fully implicit type closest point projection method (CPPM) are the two most widely used frameworks for numerical stress integration. CPM is simple, easy to implement and accurate up to first order. CPPM is unconditionally stable and accurate up to second order though the formulation is complex. Therefore, this study aims to develop a less complex and accurate stress integration method for complex constitutive models.

Two integration techniques are formulated using the midpoint and Romberg method by modifying CPM. The algorithms are implemented for three different classes of soil constitutive model. The efficiency of the algorithms is judged via stress point analysis and solving a boundary value problem.

Stress point analysis indicates that the proposed algorithms are stable even with a large step size. In addition, numerical analysis for solving boundary value problem demonstrates a significant reduction in central processing unit (CPU) time with the use of the semi-implicit-type midpoint algorithm.

Traditionally, midpoint and Romberg algorithms are formulated from explicit integration techniques, whereas the present study uses a semi-implicit approach to enhance stability. In addition, the proposed stress integration algorithms provide an efficient means to solve boundary value problems pertaining to geotechnical engineering.

This paper aims to investigate the application of adaptive integration in element-free Galerkin methods for solving problems in structural and solid mechanics to obtain accurate reference solutions.

An adaptive quadrature algorithm which allows user control over integration accuracy, previously developed for integrating boundary value problems, is adapted to elasticity problems. The algorithm allows the development of a convergence study procedure that takes into account both integration and discretisation errors. The convergence procedure is demonstrated using an elasticity problem which has an analytical solution and is then applied to accurately solve a soft-tissue extension problem involving large deformations.

The developed convergence procedure, based on the presented adaptive integration scheme, allows the computation of accurate reference solutions for challenging problems which do not have an analytical or finite element solution.

This paper investigates the application of adaptive quadrature to solid mechanics problems in engineering analysis using the element-free Galerkin method to obtain accurate reference solutions. The proposed convergence procedure allows the user to independently examine and control the contribution of integration and discretisation errors to the overall solution error. This allows the computation of reference solutions for very challenging problems which do not have an analytical or even a finite element solution (such as very large deformation problems).

Analyses several algorithms for the integration of the Jaumann stress rate. Places emphasis on accuracy and stability of standard algorithms available in commercial and government finite element codes in addition to several other proposals available in the literature. The analysis is primarily concerned with spinning bodies and reveals that a commonly used algorithm is unconditionally unstable and only first‐order objective in the presence of rotations. Other proposals are shown to have better accuracy and stability properties. Finally, shows by example that even a consistent and unconditionally stable integration of hypoelastic constitution does not necessarily yield globally stable finite element simulations.

The purpose of this paper is to suggest a robust hybrid method for updating the stress and plastic internal variables in plasticity considering damage mechanics.

By benefiting the properties of the well-known explicit and implicit integrations, a new mixed method is derived. In fact, the advantages of the mentioned techniques are used to achieve an efficient integration.

The numerical studies demonstrate the high precision and robustness of the suggested algorithm.

The perfect von-Mises plasticity together with Lemaitre damage model is considered within the realm of small deformations.

Updating stress and plastic internal variables are of utmost importance in elastoplastic analyses of structures. The accuracy and efficiency of stress-updating methods significantly affect the final outcomes of nonlinear analyses.

The idea which is used to derive the hybrid method leads to an efficient integration method for updating the constitutive equations of the damage mechanics.

This work addresses the computational aspects of a model for elastoplastic damage at finite strains. The model is a modification of a previously established model for large strain elastoplasticity described by Perić et al. which is here extended to include isotropic damage and kinematic hardening. Within the computational scheme, the constitutive equations are numerically integrated by an algorithm based on operator split methodology (elastic predictor—plastic corrector). The Newton—Raphson method is used to solve the discretized evolution equations in the plastic corrector stage. A numerical assessment of accuracy and stability of the integration algorithm is carried out based on iso‐error maps. To improve the stability of the local N—R scheme, the standard elastic predictor is replaced by improvedinitial estimates ensuring convergence for large increments. Several possibilities are explored and their effect on the stability of the N—R scheme is investigated. The finite element method is used in the approximation of the incremental equilibrium problem and the resulting equations are solved by the standard Newton—Raphson procedure. Two numerical examples are presented. The results are compared with those obtained by the original elastoplastic model.

Though the problem of resolving translational motion in particle methods is a relatively straightforward task, the complications of resolving rotational motion are non‐trivial. Many molecular dynamics and non‐deformable discrete element applications employ an explicit integration for resolving orientation, often involving products of matrices, which have well‐known drawbacks. The purpose of this paper is to investigate commonly used algorithms for resolving rotational motion and describe the application of quaternion‐based approaches to discrete element method simulations.

Existing algorithms are compared against a quaternion‐based reparameterization of both the central difference algorithm and the approach of Munjiza et al. for finite/discrete element modeling (FEM/DEM) applications for the case of torque‐free precession.

The resultant algorithms provide not only guaranteed orthonormality of the resulting rotation but also allow assumptions of small‐angle rotation to be relaxed and the use of a more accurate Taylor expansion instead.

The approaches described in this paper balance ease of implementation within existing explicit codes with computational efficiency and accuracy appropriate to the order of error in many discrete element method simulations.

The purpose of this paper is to propose multisensory integration for train positioning application, to support recent automatic train control systems and also moving block signaling systems.

Reducing the cost and at the same time improving the reliability and accuracy of the overall positioning system, are primary goals of the researches going on in this field.

This paper designs and evaluates two different algorithms of Kalman filtering (KF) and particle filtering (PF), on a set of low cost positioning systems, as tachometers, Doppler radar and balises.

This paper's research outcomes introduce considerable improvements upon the results when compared to the current utilization of the stand‐alone tachometer and Doppler radar sensors, and slight improvements in comparison with the KF algorithm, and also upon results in recent publications on the subject.

The purpose of this paper is to analyse algorithms for fluid‐structure interaction (FSI) from a purely algorithmic point of view.

First of all a 1D model problem is selected, for which both the fluid and structural behavior are represented through a minimum number of parameters. Different coupling algorithm and time integration schemes are then applied to the simplified model problem and their properties are discussed depending on the values assumed by the parameters. Both exact and approximate time integration schemes are considered in the same framework so to allow an assessment of the different sources of error.

The properties of staggered coupling schemes are confirmed. An insight on the convergence behavior of iterative coupling schemes is provided. A technique to improve such convergence is then discussed.

All the results are proved for a given family of time integration schemes. The technique proposed can be applied to other families of time integration techniques, but some of the analytical results need to be reworked under this assumption.

The problems that are commonly encountered in FSI can be justified by simple arguments. It can also be shown that the limit at which trivial iterative schemes experience convergence difficulties is very close to that at which staggered schemes become unstable.

All the results shown are based on simple mathematics. The problems are presented so to be independent of the particular choice for the solution of the fluid flow.