Gotowa bibliografia na temat „Mindlin-type solid”

Remarks concerning the analysis of thick sandwich shells are presented. The results obtained for a Mindlin type shell element and a technique which uses shell and solid elements are compared with the available analytical solution.

Delamination is one of the major failure mechanisms for composites and traditionally the simulation requires high expertise in fracture mechanics and dedicated knowledge of the Finite Element Analysis (FEA) tool. Yet, the simulation cycle times are high. Geometrically nonlinear analysis approach, which is based on the Reissner-Mindlin-Von K´arm´an type shell facet model, has been implemented into the Elmer FE solver. Altair ESAComp software runs the Elmer Solver in the background. A post-processing capability, which enables the prediction of the delamination onset from the FEA output, has been implemented into the AltairESAComp software. A Virtual Crack Closure Technique (VCCT) specifically developed for shell elements defining the Strain Energy Release Rate (SERR) related to the different delamination modes at the crack front is used. The onset of delamination is predicted using the relevant delamination criteria that utilize the SERR data and material allowables in the form of fracture toughness. The modeling methodology is presented for laminates including initial through-the-width delamination. Examples include delamination in the solid laminate and debonding of the skin laminate in the sandwich structure. Rather coarse FE mesh has proved to yield good results when compared to typical approaches that utilize the standard VCCT or Cohesive Zone Elements.

Due to the rapid development of additive manufacturing, a growing number of components in mechanical engineering are made of functionally graded materials. Compared to conventional materials, they exhibit improved properties in terms of strength, thermal, wear or corrosion resistance. However, because of the varying material properties, especially the type of in-depth grading of Young’s modulus, the solution of contact problems including the frequently encountered tangential fretting becomes significantly more difficult. The present work is intended to contribute to this context. The partial-slip contact of axisymmetric, power-law graded elastic solids under classical loading by a constant normal force and an oscillating tangential force is investigated both numerically and analytically. For this purpose, a fictitious equivalent contact model in the mathematical space of the Abel transform is used since it simplifies the solution procedure considerably without being an approximation. For different axisymmetric shaped solids and various elastic inhomogeneities (types of in-depth grading), the hysteresis loops are numerically generated and the corresponding dissipated frictional energies per cycle are determined. Moreover, a closed-form analytical solution for the dissipated energy is derived, which is applicable for a breadth class of axisymmetric shapes and elastic inhomogeneities. The famous solution of Mindlin et al. emerges as a special case.

This study aims at determining the elastic stress and displacement fields around a crack in a microstructured body under a remotely applied loading of the antiplane shear (mode III) type. The material microstructure is modeled through the Mindlin-Green-Rivlin dipolar gradient theory (or strain-gradient theory of grade two). A simple but yet rigorous version of this generalized continuum theory is taken here by considering an isotropic linear expression of the elastic strain-energy density in antiplane shearing that involves only two material constants (the shear modulus and the so-called gradient coefficient). In particular, the strain-energy density function, besides its dependence upon the standard strain terms, depends also on strain gradients. This expression derives from form II of Mindlin’s theory, a form that is appropriate for a gradient formulation with no couple-stress effects (in this case the strain-energy density function does not contain any rotation gradients). Here, both the formulation of the problem and the solution method are exact and lead to results for the near-tip field showing significant departure from the predictions of the classical fracture mechanics. In view of these results, it seems that the conventional fracture mechanics is inadequate to analyze crack problems in microstructured materials. Indeed, the present results suggest that the stress distribution ahead of the tip exhibits a local maximum that is bounded. Therefore, this maximum value may serve as a measure of the critical stress level at which further advancement of the crack may occur. Also, in the vicinity of the crack tip, the crack-face displacement closes more smoothly as compared to the classical results. The latter can be explained physically since materials with microstructure behave in a more rigid way (having increased stiffness) as compared to materials without microstructure (i.e., materials governed by classical continuum mechanics). The new formulation of the crack problem required also new extended definitions for the J-integral and the energy release rate. It is shown that these quantities can be determined through the use of distribution (generalized function) theory. The boundary value problem was attacked by both the asymptotic Williams technique and the exact Wiener-Hopf technique. Both static and time-harmonic dynamic analyses are provided.

Hierarchic shear deformable Reissner-Mindlin shell formulations possess the advantage of being intrinsically free from transverse shear locking [1], [2]. Transverse shear locking is avoided a priori through reparametrization of the kinematic variables. This reparametrization yields beam, plate and shell formulations with distinct transverse shear degrees of freedom.The efficiency of explicit dynamic analyses of thin-walled structures is limited by the critical time step size, which depends on the highest frequency of the discretized system. If Reissner-Mindlin type shell elements are used for discretization of a thin structure, the highest transverse shear frequencies limit the critical time step in explicit dynamic analyses, while being relatively unimportant for the structural response of the system. The basic idea of selective mass scaling is to scale down the highest frequencies in order to increase the critical time step size, while keeping the low frequency modes unaffected, see for instance [3]. In most concepts, this comes at the cost of non-diagonal mass matrices.In this contribution, we present recent investigations on selective mass scaling with hierarchic formulations. Since hierarchic formulations possess distinct transverse shear degrees of freedom, they offer the intrinsic ability for selective mass scaling of the shear frequency modes, while keeping the bending dominated modes mostly unaffected and retaining the diagonal structure of a lumped mass matrix. We discuss the effects of transverse shear parametrization, locking and mass lumping on the accuracy of results and a feasible time step.REFERENCES[1] R. Echter, B. Oesterle and M. Bischoff, A hierarchic family of isogeometric shell finite elements. Computer Methods in Applied Mechanics and Engineering, Vol. 254. pp. 170-180, 2013.[2] B. Oesterle, E. Ramm and M. Bischoff, A shear deformable, rotation-free isogeometric shell formulation. Computer Methods in Applied Mechanics and Engineering, Vol. 307, pp. 235-255, 2016.[3] G. Cocchetti, M. Pagani and U. Perego, Selective mass scaling and critical time-step estimate for explicit dynamics analyses with solid-shell elements. Computers and Structures, Vol. 27, pp. 39-52, 2013.