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p-Extension of C0 continuous mixed finite elements for plane strain gradient elasticity

Markolefas S., Papathanasiou T. K., Georgantzinos S. K.

Archives of Mechanics

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2019

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Vol. 71, nr 6

567--593

EN

A mixed finite element formulation is developed for the general 2D plane strain, linear isotropic gradient elasticity problem. Form II of the dipolar strain gradient theory for micro-structured solids is considered. The main variables are the double stress tensor μ and the displacement field vector u. Standard C0−continuous, high polynomial order hierarchical basis functions are employed for the finite element solution spaces (p-extension). The formulation is numerically validated against the standard axial tension patch test and the Mode I crack problem. The theoretical convergence rates of the uniform h- and p-extensions are confirmed using a benchmark problem where only double stresses appear. Results for the crack problem demonstrate that proper mesh refinement at areas of steep gradients ensures reproduction of the exact solution behaviour at different length scales. More specifically, the asymptotic exponents of the crack face opening displacement and the crack head true stress solutions of the Mode I crack problem are recovered. Finally, the upper bound of the true tensile normal stress near the crack tip is estimated. This upper bound is of major importance since the nature of the exact solution may change radically as we proceed from the macro- to micro-scale.

2

Evaluation of partial factorization for reduction of finite element matrices

Jarzębski P., Wiśniewski K.

Engineering Transactions

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2017

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Vol. 65, iss. 1

163--170

EN

In this paper, we present the concept of Partial Factorization [1] and discuss its possible applications to the Finite Element method. We consider: (1) reduction of the element tangent matrix, which is particularly important for mixed/enhanced elements and (2) reduction of the sub-domain matrices of the Domain Decomposition (DD) equation solvers run either sequentially on a single machine or in parallel on a cluster of computers. We demonstrate that Partial Factorization can be beneficial for these applications.

3

On the use of mixed finite elements in topology optimization

Cinquini C., Bruggi M.

Foundations of Civil and Environmental Engineering

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2006

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No. 7

17-33

EN

The durability of concrete structures is commonly considered in all domains of building activity. One of the promising methods for the durability improvement of concrete surface is application of controlled permeability formwork (CPF). Nowadays, a number of advanced materials designed to be effective as linings in formwork is commonly available. The actual effectiveness of such formworks depends significantly on the concrete mixture, its placing and compacting, and many other factors. Despite the good results of individual tests, many aspects of the problem have not been clarified yet. The recent tests were mostly done on specimens and very few results concerning the effects on entire members have been published so far. Apart from different tests on basic properties of concrete surface - like hardness, abrasion, tensile strength, resistance to water penetration and absorption, chloride diffusion, carbonation, frost resistance - the tests presented here were focused on the effectiveness of reduced concrete cover.

4

Mixed finite element formulation and optimal design of thin composite laminates

Cinquini C., Mariani C., Venini P.

Control and Cybernetics

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1998

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Vol. 27, no 2

165-176

EN

A Hellinger-Reissner variational principle is introduced to derive the weak form equation of thin generally orthotropic laminates. It leads naturally to a mixed finite-element approximation that has the out-of-plane deflection and the bending and twisting moments as independent unknowns. A triangular element is derived that is used for both analysis and optimization purposes. Numerical simulations on example laminates of irregular geometry are presented to validate the theoretical framework.