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Simulating multi-body dynamics with both rigid and flexible parts and with frictional contacts is a hard problem. We solve this by expressing the couplings between the bodies as position level constraints. The implicit treatment of the constraint directions gives us improved stability over velocity based methods. Then by employing regularization of nonlinear constraints and a convex minimization formulation, we bridge constraint-based methods to traditional force-based methods. In fact, the former are just a dual variables formulation of the latter. We solve this dual problem using position based dynamics (PBD). We show how PBD is a completely valid modeling technique and we extend it with an accurate contact and Coulomb friction model. We further show for the first time how the same solver can be used to simulate both rigid and deformable solids with two way coupling. For the soft bodies we introduce a novel form of linear finite elements expressed as constraints, that is more accurate than PBD mass-spring systems. More of our results include the energy conserving Newmark integrator and the accelerated Jacobi solver suitable for parallel architectures. Note that this paper is an extended and revised version of the conference paper published in [1]. [ABSTRACT FROM AUTHOR]

This paper focuses on coupling two different computational approaches, namely finite element method (FEM) and meshless finite difference method (MFDM), in one domain. The coupled approach is applied in solving thermomechanical initial–boundary value problem where the heat transport in the domain is non-stationary. In this method, the domain is divided into two subdomains for FEM and MFDM, respectively. Contrary to other coupling techniques, the approach presented in this paper is defined in terms of mathematical problem formulation rather than at the approximation level. In the weak form of thermomechanical initial–boundary value problem (variational principle), the appropriate additional coupling integrals are defined a-priori. Subsequently, the FEM and the MFDM approximations, which may differ from each other, are provided to the formulation. It is assumed that there exists a very thin layer of material between the subdomains, which is not spatially discretized. The width of this layer may be considered the coupling parameter and it is the same for both, thermal and mechanical parts. Similar approach is applied to essential boundary conditions (e.g. prescribed temperature and displacements). Consequently, the consistent formulation of the mixed problem for the coupled FEM–MFDM method is derived. The analysis is illustrated with two- and three-dimensional examples of mechanical and thermomechanical problems. [ABSTRACT FROM AUTHOR]

This paper deals with the computational modeling and numerical simulation of contact problems at finite deformations using the finite element method. Quasi-static and dynamic problems are considered and two particular frictional conditions, full stick friction and frictionless cases, are addressed. Lagrange multipliers and regularized formulations of the contact problem, such as penalty or augmented Lagrangian methods, are avoided and a new direct elimination method is proposed. Conserving algorithms are also introduced for the proposed formulation for dynamic contact problems. An assessment of the performance of the resulting formulation is shown in a number of selected benchmark tests and numerical examples, including both quasi-static and dynamic contact problems under full stick friction and frictionless contact conditions. Conservation of key discrete properties exhibited by the time stepping algorithm used for dynamic contact problems is also shown in an example. [ABSTRACT FROM AUTHOR]

In this paper, we use the finite element method (FEM) with nonlocal boundary condition for solving the nondestructive testing problem of wood moisture content based on a planar capacitance sensor model (i.e. the DtN-FEM for solving the mathematical model which is described by the exterior problems of a class of 3D Laplace equation with complicated boundary conditions). The original boundary value problem is reduced to an equivalent nonlocal boundary value problem via a Dirichlet-to-Neumann (DtN) mapping represented in terms of the Fourier expansion series. For numerical computation, a series of approximate problems with higher accuracy can be derived if one truncates the series term in the variational formulation, which is equivalent to the reduced problem. The error estimate is presented to show how the error depends on the finite element discretization and the accuracy of the approximate problem. Based on the numerical results, the relationship between the dielectric constant (DC) of tested wood and the capacitance value of the sensor is discussed. Finally, we applied a least squares fitting method (LSFM) to reconstruct the wood moisture content (WMC) from the data measured with a planar capacitance sensor. Compared with popular statistical methods, the hybrid experimental–computational method is more convenient and faster, and a large number of experiments are avoided, the costs of testing are reduced. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, a polygonal finite element method is presented for large deformation frictionless dynamic contact-impact problems with non-conformal meshes. The geometry and interfaces of the problem are modeled independent of the background mesh based on the level set method to produce polygonal elements at the intersection of the interface with the regular FE mesh. Various polygonal shape functions are employed to investigate the capability of polygonal-FEM technique in modeling frictionless contact-impact problems. The contact constraints are imposed between polygonal elements produced along the contact surface through the node-to-surface contact algorithm. Several contact-impact problems are modeled using various polygonal interpolation functions, including the Wachspress interpolation functions, the metric coordinate shape functions, the natural neighbor based functions, and the mean value coordinate functions to demonstrate the efficiency of proposed technique in modeling contact-impact problems. [Copyright &y& Elsevier]

Summary: In this paper we present a stochastic dimension reduction multiscale finite element method for solving groundwater flow problems in heterogeneous random porous media. The stochastic conductivity is parameterized in a stochastic space using a truncated Karhunen–Loève expansion with finite random variables. This often results in high stochastic dimensionality due to small correlation length and large variance of the inherent covariance function. In order to treat the high-dimensional stochastic problems efficiently, a truncated high-dimensional model representation (HDMR) technique is proposed that decomposes the high-dimensional stochastic problem into a moderate-dimensional stochastic problem and a few one-dimensional stochastic problems. The derived low-dimensional stochastic problems are solved by incorporating a sparse grid stochastic collocation method (SGSCM) with the proposed HDMR. This leads to a set of uncoupled deterministic problems at the sparse grid collocation points. To capture the small-scale heterogeneities in physical space, a multiscale finite element method (MsFEM) is utilized to solve these deterministic problems. Since the SGSCM and MsFEM are implemented in the different spaces, the integrated approach inherits the advantages from both of the SGSCM and the MsFEM, in which each low-dimensional stochastic problem is decoupled each other at small number of stochastic collocation points and is solved on a coarse spatial mesh. To demonstrate the efficiency and accuracy of the proposed stochastic MsFEM with the HDMR technique, a few numerical experiments are carried out for the transient water flow problems in heterogeneous random media with different correlation lengths and various degrees of spatial variabilities. [Copyright &y& Elsevier]

Abstract: Model updating should be correlated with experimental data to ensure that it models the dynamics of the real structure and the updated model predicts the dynamics of a structure more accurately. Considering that the iterative methods for model updating have aroused little public attention, this paper studies an iterative algorithm for quadratic model updating problems which can incorporate the measured modal data into the finite element model to produce an adjusted finite element model on the mass, gyroscopic and stiffness matrices that closely match the experimental modal data. By this method, the best approximation symmetric and skew-symmetric solutions can be obtained by choosing a convergence factor. Numerical example shows that the introduced iterative algorithm is quite efficient. [Copyright &y& Elsevier]

Abstract: This paper presents a canonical dual mixed finite element method for the post-buckling analysis of planar beams with large elastic deformations. The mathematical beam model employed in the present work was introduced by Gao in 1996, and is governed by a fourth-order non-linear differential equation. The total potential energy associated with this model is a non-convex functional and can be used to study both the pre- and the post-buckling responses of the beams. Using the so-called canonical duality theory, this non-convex primal variational problem is transformed into a dual problem. In a proper feasible space, the dual variational problem corresponds to a globally concave maximization problem. A mixed finite element method involving both the transverse displacement field and the stress field as approximate element functions is derived from the dual variational problem and used to compute global optimal solutions. Numerical applications are illustrated by several problems with different boundary conditions. [Copyright &y& Elsevier]

Abstract: In this paper a second order characteristics finite element scheme is applied to the numerical solution of natural convection problems. Firstly, after recalling the mathematical model, a second order time discretization of the material time derivative is introduced. Next, fully discretized schemes are proposed by using finite element methods. Numerical results for the two-dimensional problem of buoyancy-driven flow in a square cavity with differentially heated side walls are given and compared with a reference solution. [Copyright &y& Elsevier]

The optimization of obtaining the most uniform load distribution is important for the load carrying capacity design of the planetary roller screw mechanism (PRSM). However, the stiffness matrix of PRSM in traditional method based on the relationship between load and deformation of the thread may be destroyed when threads are no longer in contact due to machining errors, which would bring convergence problem in optimization process. In this paper, the mathematical model is firstly established to overcome the above drawbacks by proposing an improved iterative algorithm. Then, the multi-objective optimization is conducted to search the best designed pitches for the most uniform load distribution on both the screw-roller and nut-roller interfaces, and results are verified by the finite element method. • The mathematical model of load distribution considering pitch errors, pitch deviation and installation modes is established. • An improved iterative algorithm is proposed to solve the divergent problems in previous methods. • The effects of pitch errors and pitch deviation on the load distribution are is deeply studied. • The multi-objective optimization is conducted to search the best designed pitches for the most uniform load distribution of PRSM. [ABSTRACT FROM AUTHOR]