Many widely used beam finite element formulations are based either on Reissner's classical nonlinear rod theory or the absolute nodal coordinate formulation (ANCF). Advantages of second method have been pointed out by several authors; among benefits constant mass matrix ANCF elements, isoparametric approach and existence a consistent displacement field along whole cross section. Consistency allows simpler, alternative for contact problems inelastic materials. Despite conceptional differences...

In this paper, we introduce new finite elements to approximate the Hellinger Reissner formulation of elasticity. The are vector-valued tangential continuous Nédélec for displacements, and symmetric tensor-valued, normal–normal stresses. These do neither suffer from volume locking as Poisson ratio approaches ½, nor shear when anisotropic used thin structures. We present analysis elements, discuss their implementation, give numerical results.

SUMMARY In this paper, we present a family of mixed finite elements, which are suitable for the discretization slim domains. The displacement space is chosen as Nédélec's tangential continuous whereas stress approximated by normal–normal symmetric tensor‐valued elements. We show stability system on domain discretized tensor product mesh, where constant does not depend aspect ratio discretization. give interpolation operators element spaces, and thereby obtain optimal order priori error...

In many applications, thin shell-like structures are integrated within or attached to volumetric bodies. This includes reinforcements placed in soft matrix material lightweight structure design, hollow that partially completely filled. Finite element simulations of such setups highly challenging. A brute force discretization structural as well parts using well-shaped three-dimensional elements may be accurate, but leads problems enormous computational complexity even for simple models. One...

The multibody dynamics and finite element simulation code has been developed since 1997. In the past years, more than 10 researchers have contributed to certain parts of HOTINT, such as solver, graphical user interface, library, joint functionality port blocks. Currently, a script-language based version HOTINT is freely available for download, intended research, education industrial applications. main features current include objects like point mass, rigid bodies, complex point-based joints,...

A standard technique to reduce the system size of flexible multibody systems is component mode synthesis. Selected shapes are used approximate deformation each single body numerically. Conventionally, (small) added relatively a body-local reference frame which results in floating formulation (FFRF). The coupling between large rigid motion and small relative nonlinear, leads computationally expensive nonconstant mass matrices quadratic velocity vectors. In present work, total (absolute)...

A new family of locking-free finite elements for shear deformable Reissner-Mindlin plates is presented. The are based on the "tangential-displacement normal-normal-stress" formulation elasticity. In this formulation, bending moments treated as separate unknowns. degrees freedom plate element nodal values deflection, tangential components rotations and normal-normal strain. Contrary to other elements, no special treatment term such reduced integration necessary. attain an optimal order convergence.

The tangential-displacement normal-normal-stress (TDNNS) method is a finite element for mixed elasticity. As the name suggests, tangential component of displacement vector as well normal-normal stress are degrees freedom elements. TDNNS was shown to converge optimal order, and be robust with respect shear volume locking. However, slightly nonconforming, an analysis natural norms arising spaces still missing. We present sound mathematical theory infinite dimensional problem using space...

So-called electro-active polymers are not only capable of undergoing very large deformations, but they also exhibit different electromechanical coupling effects due to their dielectric or electrostrictive characteristics. In the present paper sub-class elastomers is studied; in particular, we focus on thin elastomer shells, which undergo deformations under an applied electric field. We develop a framework for modeling and subsequent efficient simulation structures made from incompressible...

Abstract Smart materials respond to external stimuli, e.g., electric fields, which enables their use as sensors and actuators. The electromechanical coupling of the direct converse piezoelectric effects, for instance, is used both actuation sensing in diverse engineering applications. response ferroelectric depends on state remanent polarization presence an field. To extend operational range actuators, accurate understanding evolution material’s imperative, requires physical geometric...

We are concerned with the mathematical modeling of polarization process in ferroelectric media. assume that this dissipative is governed by two constitutive functions, which free energy function and dissipation function. The function, closely connected to dissipated energy, usually non-differentiable. Thus, a minimization condition for overall includes subdifferential This can also be formulated way variational inequality unknown fields strain, dielectric displacement, remanent strain....

We propose a new three-dimensional formulation based on the mixed Tangential-Displacement Normal-Normal-Stress (TDNNS) method for elasticity. In elastic TDNNS elements, tangential component of displacement field and normal stress vector are degrees freedom continuous across inter-element interfaces. finite elements have been shown to be locking-free with respect shear locking in thin which makes them suitable discretization laminates or macro-fibre composites. current paper, we extend...

In industrial practice, the floating frame of reference formulation (FFRF)—often combined with component mode synthesis (CMS) in order to reduce number flexible degrees-of-freedom—is common approach describe arbitrarily shaped bodies multibody systems. Owed relative deformation respect frame, equations motion show state-dependent nonconstant inertia terms. Such description, however, comes along considerable numerical costs, since both mass matrix and gyroscopic forces, i.e., quadratic...

Recently, "Tangential Displacement Normal Stress" elements were introduced for small-deformation piezoelectric structures. Benefits of these are that they free from shear locking in thin structures and volume nearly incompressible materials. We extend to the large deformation case electro-active polymers framework an updated Lagrangian method. observe convergence does not deteriorate as material becomes with growing Lamé parameter λ, discretization slender by flat is feasible. The freely...

The buckling and postbuckling of a shear-deformable cantilever is studied using Reissner's geometrically exact relations for the planar deformation beams. subjected to compressive follower force whose line action passes through spatially fixed point. To study behavior, consistent linearization equilibrium kinematic introduced. influence shear extensibility on critical loads studied. behavior turns out crucially depend ratio between stiffness extensional structure. Closed-form solutions in...

The present article is concerned with modeling the viscoelastic behavior of Polydimethylsiloxane (PDMS) in large-strain regime. Starting from basic principles thermodynamics, an incremental variational formulation derived. Within this model, free energy density and dissipation function determine elastic viscous properties solid. main contribution paper estimation parameters proposed phenomenological model measurements conducted on Sylgard184 samples. This non-linear material simplifies to a...

Abstract The present article, provides a novel mixed finite element formulation for elastoplasticity which is suitable the discretization of thin‐walled structures using highly anisotropic volume elements. We thermodynamically consistent framework modeling elastoplastic stress response, where dissipative effects are considered through dissipation function instead explicit flow rules. Along these lines, incremental principle, in stresses included as independent unknowns, derived. propose to...

Abstract We develop an a posteriori error bound for the interior penalty discontinuous Galerkin approximation of biharmonic equation with continuous finite elements. The is based on two-energies principle and requires computation equilibrated moment tensor. natural space tensor that symmetric fields normal-normal components, well-known from Hellan-Herrmann-Johnson mixed formulation. propose construction totally local. procedure can also be applied to original Hellan–Herrmann–Johnson...

An energy-based model of the ferroelectric polarization process is presented in current contribution. In an setting, dielectric displacement and strain (or displacement) are primary independent unknowns. As internal variable, remanent vector chosen. The then governed by two constitutive functions: free energy function dissipation function. Choices for both functions given. rate-independent response non-differentiable, it proposed to regularize problem. Then, a variational equation can be...

The floating frame of reference formulation (FFRF) together with modal reduction is a standard method in multibody system dynamics. As an advantage the FFRF, fully nonlinear coupling small flexible deformations superimposed to arbitrarily large rigid body motion considered. idea present paper apply FFRF component mode synthesis electromagnetically levitated high-speed rotor, which tilting angles may occur, are not accounted for classical rotor applicability dynamics, especially close bending...