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The problem of integrating the rotational vector from a given angular velocity vector is met in such diverse fields as the navigation, robotics, computer graphics, optical tracking and non-linear dynamics of flexible beams. For example, if the numerical formulation of non-linear dynamics of flexible beams is based on the interpolation of curvature, one needs to derive the rotation from the assumed curvature field. The relation between the angular velocity and the rotation is described by the first-order quasi-linear differential equation. If the rotation is given, the related angular velocity is obtained by the differentiation. By contrast, if the angular velocity is given, the related rotations are obtained by the integration. The exact closed-form solution for the rotation is only possible if the angular velocity is constant in time. In dynamics of non-linear flexible spatial beams, the problem of integrating rotations from a given angular velocity becomes even more complex because both the angular velocity and the curvature need simultaneously be integrated and are both functions of space and time. As the angular velocity and the curvature are assumed to be analytic functions, they must satisfy certain integrability conditions to assure the unique rotation is obtained from the two differential equations. The objective of the present paper is to derive approximate, yet closed-form solutions of the following problem: for a given curvature vector, determine both the rotation and the angular velocity. In order to avoid the singularity of kinematic relations, the quaternions are used for the parametrization of rotations, and the integrations are partly performed in the four-dimensional quaternion space. The resulting closed-form expressions for the rotational and angular velocity quaternions are ready to be used in the finite-element formulations of the dynamics of flexible spatial beams as interpolating functions. The present novel solution is assessed by comparisons of the numerical results with analytical solutions for variety of oscillating curvature functions, as well as with the solutions of the quaternion-based midpoint integrator and the Runge–Kutta-based Crouch–Grossman geometrical methods CG3 and CG4. [ABSTRACT FROM AUTHOR]

A new semi-analytical procedure is derived for the determination of buckling of the reinforced concrete column exposed to fire. The fire analysis is performed in three separate steps, of which the time development of temperatures in the fire compartment is performed first, followed by the coupled heat and moisture transfer analysis and, finally, by the mechanical analysis. A particular emphasis has been given to the critical buckling time and the remaining critical buckling load at a selected time. For this purpose, a parametric study has been performed by which the influence of different geometric parameters on the buckling load capacity of reinforced concrete columns has been assessed. The results of this study show that the load-carrying capacity of the column reduces significantly with the increasing time of fire exposure and the column slenderness. Moreover, the initial mechanical load has a small, although not negligible effect on the buckling load capacity. [ABSTRACT FROM AUTHOR]

A three-step model for the performance-based numerical simulations of the fire response of steel–RC two-layered beam-like composite structures is presented and validated. The first step consists of the determination of the evolution of temperatures in the structure׳s surroundings. Moisture and the heat transfer through the RC layer and the conduction of heat over the steel layer are obtained in the second step. In concrete, the transfer of water vapour, dry air, and free water is discussed as well as the evaporation and liquefaction phenomena and the dehydration of concrete and its thermal and mechanical degradation. Within the framework of the third step, a geometrically and materially non-linear mechanical response of the structure is proposed accounting for interlayer slips and uplifts as well as for various material-related phenomena such as the material hardening/softening and creep. The governing equations are solved numerically. An efficient, novel strain-based finite element formulation is introduced for the mechanical analysis. Due to its generality and consideration of several different possible non-linear material, geometrical, and interlayer contact phenomena and their couplings the model can be of a use to a broader fire science community for exploring the impact of different physical parameters on the results of the addressed numerical simulations, thereby providing directions for further research. In the paper a case of such a study is also demonstrated exploring the contribution of the steel sheet and the flexibility of the interlayer connection of a standard trapezoidal steel–RC slab to its ultimate fire resistance. A reasonable contribution of the sheet is proved if the stiffness ratio between the integrated and the external tensile reinforcement of the RC plate is low provided that the contact connection is sufficiently stiff. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents a new finite-element formulation for the dynamic analysis of three-dimensional beams. The formulation is based on the geometrically exact three-dimensional beam theory in which the strain vectors are the only unknown functions of the arc-length parameter. The classical Newmark time integration scheme extended to the multiplicative group of spatial rotations is used and properly adapted for the strain-based formulation. The Generalized- method is used to enforce a numerical dissipation of higher modes. The update procedure needed in the iteration process is discussed in detail. The exact linearization of the governing equations is also presented. The performance of the formulation is demonstrated with numerical examples. [Copyright &y& Elsevier]

Abstract: Failure of concrete under compression results in a localized region of softened material subject to high strain. The paper attempts to find out the error of the numerical method for the mechanical analysis of planar reinforced-concrete beams subject to temperature increase simulating typical fire conditions at high temperatures, if the strain softening in concrete is considered, while employing continuous finite elements. The results are confronted with the formulation using constant-strain crack band elements in the localized regions combined with the continuous elements everywhere else. The width of the crack band is, in principle, temperature and stress–state dependent. In the paper we assume the crack band elements of constant width throughout the analysis, which may be a valid assumption at high temperatures, as indicated by some data given in literature. Results of the analyses of a two-story, two-bay reinforced concrete frame, designed strictly in accordance with the European standards, and subject to self weight, dead and service loads and, additionally, to the increasing fire-like thermal load are presented. The use of solely continuous finite elements, yet accounting for strain softening of material wherever it occurs, yields spatially oscillating results for strains around the localized region. This sometimes yields a totally false result or loss of convergence of the global Newton method. The width of the localized band tends to zero with the growing density of the finite-element mesh, with the results being highly mesh sensitive. The finite-element meshes where constant-strain crack band elements in the localized regions are combined with the continuous elements everywhere else yield, on the other hand, a computationally stable and accurate post-instability response for a wide range of crack-band element widths. Its critical point is, however, obtaining a reliable estimate of the width of the crack band element at high temperatures. This requires extensive experimental testing with hot concrete in compression. [Copyright &y& Elsevier]

Abstract: The rotational quaternions are the unique four-dimensional representation of rotations in three-dimensional Euclidean space. In the present paper on the dynamics of non-linear spatial beams, they are used as the basic rotational parameters in formulating the finite-element approach of geometrically exact beam-like structures. The classical concept of parametrizing the rotation matrix by the rotational vector is completely abandoned so that the only rotational parameters are the rotational quaternions representing both rotations and rotational strains in the beam. Because the quaternions are the elements of a four-dimensional linear space, their use is an advantage compared to the elements of the special orthogonal group . This makes possible, e.g. to interpolate the rotational quaternions in a standard additive way and to apply standard Runge–Kutta time integration methods. The present finite-element realization of such a quaternion-based beam theory introduces some further ideas including the use of collocation, the weak form of the consistency equations and the symmetrically integrated boundary conditions which enhances the accuracy or efficiency of the solution and avoids the differential–algebraic type of the discretized governing equations often met in classical formulations. The main advantage of the proposed dynamics formulation is probably its simple implementation into the standard Runge–Kutta procedures. Thus several benefits of the Runge–Kutta methods such as the absence of the analytical linearization of the discrete governing equations, the local error control and the adaptive time steps are automatically incorporated in the present procedure. [Copyright &y& Elsevier]

Abstract: The paper presents a formulation of the geometrically exact three-dimensional beam theory where the shape functions of three-dimensional rotations are obtained from strains by the analytical solution of kinematic equations. In general it is very demanding to obtain rotations from known rotational strains. In the paper we limit our studies to the constant strain field along the element. The relation between the total three-dimensional rotations and the rotational strains is complicated even when a constant strain field is assumed. The analytical solution for the rotation matrix is for constant rotational strains expressed by the matrix exponential. Despite the analytical relationship between rotations and rotational strains, the governing equations of the beam are in general too demanding to be solved analytically. A finite-element strain-based formulation is presented in which numerical integration in governing equations and their variations is completely omitted and replaced by analytical integrals. Some interesting connections between quantities and non-linear expressions of the beam are revealed. These relations can also serve as useful guidelines in the development of new finite elements, especially in the choice of suitable shape functions. [Copyright &y& Elsevier]

Abstract: A new mathematical model for the non-linear analysis of two-layer planar beams considering flexible connections is introduced and an effective, strain-based finite element numerical solution method derived. The model and the solution method account for the exact geometrically non-linear behaviour in each separate layer. Material is assumed homogeneous but can be different in each layer. The shear strains are neglected. The laws of contact in both tangent and normal directions are taken non-linear. Numerical examples verify the proposed approach. The comparisons with numerical and experimental results from literature are made and the effects of uplift on ductility and stress distribution in beams are systematically explored. The theoretical model, combined with the present numerical formulation, has been found to result in realistic behaviour, while the numerical method proves to be accurate, reliable and computationally effective. [Copyright &y& Elsevier]

Abstract: The present paper presents a consistent model of a three dimensional delaminated composite column with a proper consideration of the extensional and bending stiffness coupling and transverse shear effect to determine the axial buckling load. The exact analytical solution of the buckling force is obtained using the linearized stability theory. The three dimensional model allows us to consider a rather general set of delaminations including those that are not necessarilly perpendicular to the symmetry axis of the cross-section or/and have non-symmetrical surfaces. The parametric studies are presented showing the effects of shear, the delamination position, the angle of rotation of the delamination and the ratio of elastic to shear moduli. [Copyright &y& Elsevier]

Size, shape, and drive optimization procedures are combined with an energy-conserving time-integration scheme for the dynamic analysis of planar geometrically non-linear frame structures undergoing large overall motions. The solution method is based on the finite-element formulation, employing the classical displacement-based planar beam finite elements described in an inertial frame. Finite axial, bending, and shear strains are taken into account. If the system is conservative, the energy and momenta conservation in the discrete system during motion is guaranteed. Size, shape, and drive design variables are introduced into the model. Shape parameterization is achieved by the design element technique, using Bezier patches. The sensitivity analysis is performed by the discrete approach and the analytical direct differentiation method. A gradient-based optimization method, using an automatically adjustable convex approximation technique, is employed. The efficiency and the applicability of the approach are demonstrated via numerical examples. The shape and the driving function of a load-moving robot arm are optimized to reduce oscillations in its final position. The shape of a steel frame is optimized to reduce oscillations after an idealized ground motion jerk. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents the equations for the implementation of rotational quaternions in the geometrically exact three-dimensional beam theory. A new finite-element formulation is proposed in which the rotational quaternions are used for parametrization of rotations along the length of the beam. The formulation also satisfies the consistency condition that the equilibrium and the constitutive internal force and moment vectors are equal in its weak form. A strict use of the quaternion algebra in the derivation of governing equations and for the numerical solution is presented. Several numerical examples demonstrate the validity, performance and accuracy of the proposed approach. [Copyright &y& Elsevier]

Abstract: The way the non-linear constitutive equations in the spatial beam formulations are solved, influences the rate of convergence and the computational cost. Three different approaches are studied: (i) the direct global approach, where the constitutive equations are taken to be the iterative part of the global governing equations, (ii) the local (or indirect global) approach, where the constitutive equations are solved separately in each step of the global iteration, and (iii) the partly reduced approach, which is the combination of (i) and (ii). The approaches are compared with regard to the number of global iterations and the total number of floating point operations. The direct global approach is found to be the best choice. [Copyright &y& Elsevier]

Abstract: The exact analytical solution of buckling in beams with multiple delaminations is presented. In order to investigate analytically the influence of axial and shear strains on buckling loads, the geometrically exact beam theory is employed with no simplification of the governing equations. The critical forces are then obtained by the linearized stability theory. The parametric studies are designed so that they give us fundamental understanding of the effects of the delamination number, length and position on the buckling load. The effect of shear is found to be of substantial importance. [Copyright &y& Elsevier]

Abstract: The exact analytical solution of buckling in delaminated columns is presented. In order to investigate analytically the influence of axial and shear strains on buckling loads the geometrically exact beam theory is employed with no simplification of the governing equations. The critical forces are then obtained by the linearized stability theory. In the paper, we limit the studies to linear elastic columns with a single delamination, but with arbitrary longitudinal and vertical asymmetry of delamination and arbitrary boundary conditions. The studies of quantitative and qualitative influence of transverse shear are shown in detail and extensive results for buckling loads with respect to delamination length, thickness and longitudinal position are presented. [Copyright &y& Elsevier]

We present a new strain-based finite element formulation for the dynamic analysis of highly flexible elastic planar beams. The formulation employs the geometrically exact Reissner planar beam theory which accounts for finite displacements and rotations, and finite membrane, shear and bending strains. The system of semi-discrete dynamic equations of motion is derived from the modified Hamilton principle in which only the strain variables are interpolated. Such a choice of the interpolated variables is an advantage over approaches, in which the displacements and rotations are interpolated, since the field consistency problem and related locking phenomena do not arise. The performance and accuracy of the formulation are illustrated by several numerical examples. [Copyright &y& Elsevier]

Abstract: A new locking-free strain-based finite element formulation for the numerical treatment of linear static analysis of two-layer planar composite beams with interlayer slip is proposed. In this formulation, the modified principle of virtual work is introduced as a basis for the finite element discretization. The linear kinematic equations are included into the principle by the procedure, similar to that of Lagrangian multipliers. A strain field vector remains the only unknown function to be interpolated in the finite element implementation of the principle. In contrast with some of the displacement-based and mixed finite element formulations of the composite beams with interlayer slip, the present formulation is completely locking-free. Hence, there are no shear and slip locking, poor convergence and stress oscillations in these finite elements. The generalization of the composite beam theory with the consideration of the Timoshenko beam theory for the individual component of a composite beam represents a substantial contribution in the field of analysis of non-slender composite beams with an interlayer slip. An extension of the present formulation to the non-linear material problems is straightforward. As only a few finite elements are needed to describe a composite beam with great precision, the new finite element formulations is perfectly suited for practical calculations. [Copyright &y& Elsevier]

Abstract: This paper presents the equations of the linearized geometrically exact three-dimensional beam theory of naturally curved and twisted beams. A new finite-element formulation for the linearized theory is proposed in which the strain vectors are the only unknown functions. The linear form of the consistency condition that the equilibrium and the constitutive internal force and moment vectors are equal, is enforced to be satisfied at chosen points. An arbitrary curved and twisted axis of the beam is taken into account which demands proper consideration of the non-linearity of spatial rotations. The accuracy and the efficiency of the derived numerical algorithm are demonstrated by comparing present numerical results with various analytical and numerical results. [Copyright &y& Elsevier]

Abstract: This paper presents a novel stress field and tangent material moduli integration procedure over a cross-section of a biaxially loaded concrete beam. The procedure assumes a sufficiently simple analytical form of the constitutive law of concrete, the polygonal shape of the boundary of the simply- or multi-connected cross-section and the monotonically increasing loading. The area integrals are transformed into the boundary integrals and then integrated analytically. The computational efficiency of the procedure is analyzed by comparing it with respect to the number of floating-point operations needed in various numerical integration-based methods. It is found that the procedure is not only exact, but also computationally effective. [Copyright &y& Elsevier]

A family of new beam finite elements for geometrically and materially non-linear static analysis of reinforced concrete planar frames is derived, in which strain measures are the only interpolated unknowns, and where the constitutive and equilibrium internal forces are equal at integration points. The strain-localization caused by the strain-softening at cross-sections is resolved by the introduction of a `short constant-strain element''. Comparisons between numerical and experimental results on planar frames in pre- and post-critical states show both good accuracy and computational efficiency of the present formulation. [Copyright &y& Elsevier]

Abstract: This paper introduces a new finite element formulation of the ‘geometrically exact finite-strain beam theory’. The formulation employs the generalized virtual work principle. In the resulting governing equations of the beam, the strain vectors are the only unknown functions. The consistency condition that the equilibrium and the constitutive internal force and moment vectors are equal, is enforced to be satisfied at chosen points. The accuracy and the efficiency of the derived numerical algorithm are demonstrated by several examples. [Copyright &y& Elsevier]

Abstract: A new finite element formulation is presented for the non-linear analysis of two-layer composite planar frames with an interlayer slip. For each layer the geometrically non-linear Reissner’s beam theory is assumed. A small slip between the layers is considered. Non-linear, time-dependent constitutive models for the layers, and a non-linear relationship between the slip and the shear stress at the interface are accounted for. As only a few finite elements are needed to describe a beam or column of a frame with great precision, the new finite element formulation is prefectly suited for practical calculations. [Copyright &y& Elsevier]

The standard test problem of MacNeal and Harder (Finite Elem. Anal. Des. 1 (1985) 3) for the verification of spatial beam finite elements, i.e. the deflection of the initially twisted beam, is commented through the analysis of three variants of initially twisted beams: (i) a linearly twisted beam with a constant cross-section; (ii) a non-linearly twisted beam with a constant cross-section; and (iii) a non-linearly twisted beam with variable cross-sections. Our numerical results lead to the conclusion that the twisted beam problem (Finite Elem. Anal. Des. 1 (1985) 3) assumes the linearly twisted, curved-edge beam. [Copyright &y& Elsevier]

This paper presents a new finite element formulation of the ‘geometrically exact finite-strain beam theory’. The governing equations of the beam element are derived in which the strain vectors are the only unknown functions. The consistency condition that the equilibrium and the constitutive internal force and moment vectors are equal, is enforced to be satisfied at chosen points. The solution is found by a collocation algorithm. The linearity of the strain space not only simplifies the application of Newton’s method on the non-linear configuration space, but also leads to the strain-objectivity of the proposed method. The accuracy and the efficiency of the derived numerical algorithm are demonstrated by several examples. [Copyright &y& Elsevier]

The article introduces a new finite element formulation of the three-dimensional ‘geometrically exact finite-strain beam theory’. The formulation employs the generalized virtual work principle with the pseudo-curvature vector as the only unknown function. The solution of the governing equations is obtained by using a combined Galerkin-collocation algorithm. The collocation ensures that the equilibrium and the constitutive internal force and moment vectors are equal at a set of chosen discrete points. In Newton’s iteration special update procedures for the pseudo-curvature and rotational vectors have to be employed because of the non-linearity of the configuration space. The accuracy and the efficiency of the derived numerical algorithm are demonstrated by several examples. [Copyright &y& Elsevier]

Provides several conditions for the existence and uniqueness of the classical and generalized solutions of a planar elastic, Reissner-type cantilever beam. Basic equations of Reissner's elastica; Development of the beam theory; Importance of finite element methods in solving the equations of beam theories; Functions of the Reissner's model.

Abstract: A new finite element model for steel–concrete side-plated beams exposed to mechanical and thermal loading is presented. The moisture and heat transfer through concrete is considered independent on mechanical deformations. The hygro-thermo-mechanical analysis is performed in two separate steps starting with the moisture and heat transfer analysis and continuing with the mechanical stress–strain analysis. The finite-element model of Davie, Pearce, and Bićanić was implemented for the moisture and heat transfer analysis in the concrete part of the beam. The Fourier equation of heat transfer for non-porous solids was applied in the steel part. A novel, strain-based finite-element formulation of the planar beam is proposed to perform the mechanical part of the fire analysis. Each of the two steps of the model is first verified by comparing the present numerical results with the experimental and numerical data available in the literature. The finite-element formulations of both the hygro-thermal and the mechanical steps of the analysis are found to be reliable and accurate. Finally, effects of the side reinforcing of a RC beam as one of the methods of structural retrofitting are explored in the case of a typical fire scenario and an important contribution of the side-plates to the ultimate fire resistance of the beam is discovered, particularly when higher levels of the service load are applied to the beam. [Copyright &y& Elsevier]

Abstract: We have derived a one-dimensional mathematical model and a numerical procedure for the non-linear static analysis of pre-tensioned concrete planar beams, which intends to describe quantitatively the global behaviour as well as some local phenomena in the beam, such as the tangential slip and the traction between the tendon and concrete, with accuracy sufficient for engineering design. The advantage of such a model is its extreme computational efficiency compared to the two- and three-dimensional formulations. A shear-stiff, kinematically exact planar beam theory is used to model each component of the beam. The bending moment in the tendon is neglected. Cracking of concrete is accounted for using the smeared crack concept. Softening of material, and the related localisation of deformations, is in the numerical solution resolved by the combined use of the arc-length method and the constant strain crack band element, whose dimension is related to the fracture energy of concrete in tension. The tangential slip between the tendon and concrete is fully accounted for, yet the normal separation is not allowed. The model enables us to analyse the variation of slip and the tangential traction on tendons as well as softening of concrete in both tension and compression along the beam axis and in time. The validity of the present one-dimensional model is verified on two pre-stressed simply supported beams previously experimentally and computationally studied in literature (Rabczuk and Eibl, 2004 [2]; Rabczuk et al., 2005 [18]; Rabczuk and Belytschko, 2006 [20]). It is found out that the results of the present one-dimensional model are well in keeping with the experimental and numerical results from literature. Recalling the extreme computational efficiency of the present formulation compared to the 2D and 3D formulations it is concluded that the proposed method of analysis could be very convenient for engineering design. [Copyright &y& Elsevier]

Abstract: This paper presents a mathematical model for investigating the buckling of geometrically perfect, materially and kinematically non-linear, locally weakened reinforced concrete columns. The present analytical model is based on the linearized stability theory and is capable of predicting exact buckling loads. Based on a systematic parametric analysis, the effects of the weakness location, its magnitude, the number of weaknesses and the material non-linearity of concrete and reinforcing steel on buckling loads have been investigated. The results are given in terms of graphs showing in detail that the material non-linearity of concrete and reinforcing steel and the local weaknesses have a significant influence on the buckling load. [Copyright &y& Elsevier]

Abstract: A new mathematical model and its finite element formulation for the non-linear analysis of mechanical behaviour of a two-layer timber planar beam is presented. A modified principle of virtual work is employed in formulating the finite element method. The basic unknowns are strains. The following assumptions are adopted in the mathematical model: materials are taken to be non-linear and can differ from layer to layer; interacting shear and normal contact tractions between layers are derived from the non-linear shear contact traction–slip and the non-linear normal contact traction–uplift characteristics of the connectors; the geometrically linear and materially non-linear Bernoulli’s beam theory is assumed for each layer. The formulation is found to be accurate, reliable and computationally effective. The suitability of the theory is validated by the comparison of the numerical solution and the experimental results of full-scale laboratory tests on a simply supported beam. An excellent agreement between measured and calculated results is observed for all load levels. The further objective of the paper is the analysis of the effect of different normal contact traction–uplift constitutive relationships on the kinematic and static quantities in a statically determined and undetermined structure. While the shear contact traction–slip constitutive relationship dictates the deformability of the composite beam and has a substantial influence on most of the static and kinematic quantities of the composite beam, a variable normal contact traction–uplift constitutive relationship is in most cases negligible. [Copyright &y& Elsevier]

Abstract: This paper presents an effective computational method for non-linear analysis of composite timber beams with interlayer slips. In order to analyse such a composite structure with sufficient accuracy, a new strain based finite element was developed. The method is validated by comparison with experimentally obtained data. Four two-layer timber composite beams were tested and results compared with the numerical solution. Comparison of experimental and numerical results shows that the timber constitutive law and the contact constitutive law significantly influence the behaviour of composite timber beams. There is good agreement of measured and numerically evaluated interlayer slips at the interface surface. [Copyright &y& Elsevier]

A heuristic viscosity-type dissipation of strains is applied for controlling high frequency oscillation damping in a one-step time integration. The basic idea of the approach is to apply damping in locations, where it is needed, at times when it is needed. To this end a computationally efficient algorithm for identifying the need for damping is developed. The identification algorithm keeps track of the number of recent changes of signs of strain increments, which helps in decision whether damping should be engaged or not. A special scaling function is introduced to smoothen the transition between the damped and undamped phases. The approach is verified in the analysis of the geometrically exact plane elastic beam. [ABSTRACT FROM AUTHOR]

Abstract: We present a strain-based finite-element formulation for the dynamic analysis of flexible elastic planar multibody systems, composed of planar beams. We consider finite displacements, rotations and strains. The discrete dynamic equations of motion are obtained by the collocation method. The strains are the basic interpolated variables, which makes the formulation different from other formulations. The further speciality of the formulation is the strong satisfaction of the cross-sectional constitutive conditions at collocation points. In order to avoid the nested integrations, a special algorithm for the numerical integration over the length of the finite element is proposed. The midpoint scheme is used for the time integration. The performance of the formulation is illustrated via numerical examples, including a stiff multibody system. [Copyright &y& Elsevier]

An energy conserving finite-element formulation for the dynamic analysis of geometrically non-linear beam-like structures undergoing large overall motions has been developed. The formulation uses classical displacement-based planar beam finite elements described in an inertial frame. It takes into account finite axial, bending and shear strains. A theoretically consistent approach is used to derive a novel and simple energy conserving scheme, using the unconventional incremental strain update rather than the standard strong form. Numerical examples demonstrate perfect energy and momenta conservation, stability and robustness of the scheme, and good convergence properties in terms of both the Newton–Raphson method and time step size. [Copyright &y& Elsevier]

When some critical condition is reached at a material point of a solid body, a localized strain starts developing which makes the strain field discontinuous and highly accelerates local damaging of material. The present paper addresses this kind of strain localization in spatial geometrically exact beams. Here we propose a new beam finite element formulation which accounts for softening of material by applying the embedded strong strain discontinuity technology. The formulation is essentially an extension of the original strain-based formulation, upgraded such to allow for detecting the onset of strain localization and to introduce additional equations for evaluating singular strain peaks and jumps of displacements and rotations at the localized section in further deformation. The consistency condition that the equilibrium and the constitutive stress-resultants are equal is shown to be naturally suited for the implementation into the discontinuous formulation. The condition for the onset of strain localization at a beam cross-section is here related to the loss of uniqueness of the beam cross-sectional constitutive equations. If the condition for a unique inverse is violated, two solutions are possible for cross-sectional strains. In a subsequent deformation, one of the two solutions follows the softening regime of material. The discontinuous increments in strains, displacements and rotations at the softening cross-section are obtained from the equations of the structure supplemented by the consistency conditions of the softening cross-section. [ABSTRACT FROM AUTHOR]

A new finite element model for the analysis of the restrained curved reinforced-concrete (RC) beams simultaneously exposed to mechanical and extreme fire-like thermal loading is presented. The moisture and heat transfer through concrete is considered to be uncoupled with the deformation and the shape change of the beam. The hygro–thermo-mechanical analysis is performed in two separate steps, the first one starting with the coupled moisture and heat transfer analysis, and the next one continuing with the mechanical stress–strain analysis. A novel, strain-based finite element formulation of the curved planar beam has been developed for the mechanical part of the fire analysis. The unilateral soil–concrete beam contact is modelled with the set of discrete non-linear springs situated at nodes of the finite element mesh at the soil–beam contact. The model is verified by the numerical results of a full three-dimensional solid finite element model created in the LUSAS finite element analysis software and they are in good agreement with the present solution. In the subsequent parametric studies, the effects of material parameters of soil dictating the unilateral restraining forces to the beam, the load magnitude and the boundary conditions on the behaviour of the curved reinforced-concrete RC beam exposed to fire are investigated. [ABSTRACT FROM AUTHOR]

Introduction Education is growing to a European level with the development of student exchanges. The EFPT Exchange Programme is the first psychiatric exchange programme to be developed in Europe. It was launched in 2011 by the EFPT Exchange Programme Working Group. Objectives To provide European psychiatric trainees with the possibility of intercultural professional experience with a simplified exchange procedure. Aims To promote acquaintance of different health systems and psychiatric practices as well as cooperation among trainees, with a focus on individual experience. Methodes The programme is run by trainees, for trainees, and provides observatory internships of 2-6 weeks in psychiatric units accredited for education. We collected systematic online feedback on participant satisfaction, as well as data on countries of residence, countries of exchange and number of applicants per phase. Results Since 2011, the program has extended to 11 countries and offers 50 placements in diverse clinical psychiatry units accredited for education. Six phases of exchange have been conducted, with a total of 85 exchanges. We observed an average of 34 applications per phase with 70% of applicants originating from: Turkey, UK, Portugal, Ireland, Romania, France, Croatia. 46% of applicants were accepted for exchange. The large number of trainees underlines the richness of professional exchange and the positive effect on personal development. Conclusions The succes of this programme among trainees should encourage the promotion of mobility in psychiatric training. [ABSTRACT FROM AUTHOR]

Introduction: This is the first European psychiatric exchange programme and it aims to promote an intercultural professional exchange and cooperation among psychiatric trainees across Europe, with a focus on individual experience. Objectives: To provide trainees with the opportunities to: [•] promote awareness of intercultural aspects of psychiatry [•] engage in clinical, and/or research, and/or teaching activities [•] become acquainted with different mental health systems [•] gain experience of different illness manifestations and treatment options [•] experience a different training programme [•] socialise with peer group, promote networking and discuss coping strategies regarding work life balance Methods: The programme was developed by the exchange working group of the EFPT in 2011 and it offers 2-6 weeks in observational placements across Europe in diverse areas. Results: Feedback from pilot phase (January-July 2012) has shown excellent overall satisfaction of participants in the project. In the 2nd phase (August-December 2012) the programme has expanded offering more observational placements in 8 countries such as: Croatia, Denmark, France, Italy, Portugal, Slovenia, Spain and UK. In the 3rd phase (January-July 2013) it expanded further to include Ireland, Netherlands and Romania in a total of 11 hosting countries. Placements are offered in many subspecialties such as: psychotherapy, emergency psychiatry, child and adolescent psychiatry, eating disorders, family therapy, liaison psychiatry and psychosomatics, drug addictions, learning disabilities, forensic psychiatry and old age psychiatry. Conclusions: We hope that the diversity of placements offered by this innovative programme will constitute a new approach to the improvement of psychiatric training and practice across Europe. [Copyright &y& Elsevier]