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In this paper a smoothing procedure is suggested for the 3D beam-to-beam contact. A smooth segment is defined basing on current position vectors of three nodes limiting two adjacent finite elements. The approximated fragment of a beam axis as a 3D curve spans between the centre points of these elements. The curve is described parametrically using three Hermite polynomials. The four boundary conditions necessary to determine the coefficients for each of these polynomials involve co-ordinates and slopes at the curve ends. The slopes are defined in terms of the element nodal co-ordinates, too. There is no dependence on nodal rotations so this formulation can be embedded in a beam analysis using any type of beam finite element. This geometric representation of the curve is incorporated into the 3D beam-to-beam frictional contact model with the penalty method used to enforce contact constraints. The residual vector and the corresponding tangent stiffness matrix are determined for the normal part of contact and for the stick or slip state of friction. A few numerical examples are presented to show the performance of the suggested smoothing procedure in the cases featuring large frictional sliding. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we will derive a solver for a symmetric strongly nonsingular higher order generator representable semiseparable plus band matrix. The solver we will derive is based on the Levinson algorithm, which is used for solving strongly nonsingular Toeplitz systems. In the first part an solver for a semiseparable matrix of semiseparability rank p is derived, and in a second part we derive an solver for a band matrix with bandwidth . Both solvers are constructed in a similar way: firstly a Yule–Walker-like equation needs to be solved, and secondly this solution is used for solving a linear equation with an arbitrary right-hand side. Finally, a combination of the above methods is presented to solve linear systems with semiseparable plus band coefficient matrices. The overall complexity of this solver is plus lower order terms. In the final section numerical experiments are performed. Attention is paid to the timing and the accuracy of the described methods. [Copyright &y& Elsevier]

The present review paper examines the use of different types of polymeric matrix composites in hard tissue replacement applications. The review presents the actual state of the art in the fields of bioinert composites for permanent applications, biodegradable matrix composites for temporary applications and the emerging area of injectable composites. In all cases some recent developments are also discussed. The paper starts with an introduction to locate the reader. Bone–analogue composites are then extensively discussed. Several other systems based on an inert polymeric matrix are described, focusing on their proposed applications. A great emphasis is afterwards given to biodegradable matrix systems. The most widely used synthetic bioresorbable systems are analysed and compared with an example of natural origin degradable composites–starch based composites. Finally, composite systems that are non-processable by melt based routes and in many cases injectable are discussed in detail, including several recent developments on this emerging area of research. [Copyright &y& Elsevier]

We model the folding of ordinary paper via piecewise isometries R2→R3. The collection of crease lines and vertices in the unfolded paper is called the crease pattern. Our results generalize the previously known necessity conditions from the more restrictive case of folding paper flat (into R2); if the crease pattern is foldable, then the product (in a non-intuitive order) of the associated rotational matrices is the identity matrix. This condition holds locally in a multiple vertex crease pattern and can be adapted to a global condition. Sufficiency conditions are significantly harder, and are not known except in the two-dimensional single-vertex case. [Copyright &y& Elsevier]