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This paper aims to investigate the need for active boundary conditions during fire testing of structural elements, review existing studies on hybrid fire testing (HFT), a technique that would ensure updating of boundary conditions during a fire test, and propose a compensation scheme to mitigate instabilities in the hybrid testing procedure.

The paper focuses on structural steel columns and starts with a detailed literature review of steel column fire tests in the past few decades with varying axial and rotational end restraints. The review is followed with new results from comparative numerical analyses of structural steel columns with various end constraints. HFT is then discussed as a potential solution to be adapted for fire testing of structural elements. Challenges in contemporary HFT procedures are discussed, and application of stiffness updating approaches is demonstrated.

The reviewed studies indicate that axial and rotational restraints at the boundaries considerably influence the fire response of steel columns. Equivalent static spring technique for simulating effect of surrounding frame on an isolated column behavior does not depict accurate buckling and post-buckling response. Additionally, numerical models that simulate fire performance of a column situated in a full-frame do follow the trends observed in actual test results up until failure occurs, but these simulations do not necessarily capture post-failure performance accurately. HFT can be used to capture proper boundary conditions during testing of isolated elements, as well as correct failure modes. However, existing studies showed cases with instabilities during HFT. This paper demonstrates that a different stiffness updates calculated from the force-displacement response history of test specimen at elevated temperature can be used to resolve stability issues.

The paper has two contributions: it suggests that the provision of active boundary conditions is needed in structural fire testing, as equivalent static spring does not necessarily capture the effect of surrounding frame on an isolated element during a fire test, and it shows that force-displacement response history of test specimen during HFT can be used in the form of a stiffness update to ensure test stability.

The purpose of this paper is to introduce a method for stiffness modeling, identification and updating of collaborative robots (cobots). This method operates in real-time and with high precision and can eliminate the modeling error between the actual stiffness model and the theoretical stiffness model.

To simultaneously ensure the computational efficiency and modeling accuracy of the stiffness model, this method introduces the finite element substructure method (FESM) into the virtual joint method (VJM). The stiffness model of the cobots is built by integrating several 6-degree of freedom virtual joints that represent the elastic deformation of the cobot modules, and the stiffness matrices of these modules can be identified and obtained by the FESM. A model-updating method is proposed to identify stiffness influence coefficients, which can eliminate the modeling error between the actual prototype model and the theoretical finite element model.

The average relative error and the cycle time of the proposed method are approximately 6.14% and 1.31 ms, respectively. Compared with other stiffness modeling methods, this method not only has high modeling accuracy in high dexterity poses but also in low dexterity poses.

A hybrid stiffness modeling method is introduced to integrate the modeling accuracy of the FESM into the VJM. Stiffness influence coefficients are proposed to eliminate the modeling error between the theoretical and actual stiffness models.

The present paper is directed towards elasto‐plastic large deformation analysis of thin shells based on the concept of degenerated solids. The main aspect of the paper is the derivation of an efficient computational strategy placing emphasis on consistent elasto‐plastic tangent moduli and stress integration with the radial return method under the restriction of ‘zero normal stress condition’ in thickness direction. The advantageous performance of the standard Newton iteration using a consistent tangent stiffness matrix is compared to the classical scheme with an iteration matrix based on the infinitesimal elasto‐plastic constitutive tensor. Several numerical examples also demonstrate the effectiveness of the standard Newton iteration with respect to modified and quasi‐Newton methods like BFGS and others.

The present paper proposes a procedure for the resolution of non‐linear structural problems. It includes a study of the reliability of the results and the adaptive meshing. The iterative phase of the solution of the equilibrium equations entails an adaptive strategy for updating the tangent stiffness matrix, with a control of the load step. This results in a higher rate of convergence for the iterative process. The mechanical deformation processes here considered may give rise to considerable geometric distortion in the finite elements of the mesh. If they do, the consequence will be not only that the FE analysis fails to yield precise results, but also, owing to problems deriving from the numerical ill‐conditioning, that continuation may be impractical. To facilitate the study of these results, we developed an error estimator of the flux projection type, which is based on the mechanical deformation power. It is also used as a refinement criterion for the FE mesh. Distorted meshes can be fully or partially submitted to a process of regularization based on the aspect ratio of their elements. The mesh contour may be affected by the refinement and regularization processes, for which reason we developed a procedure for its updating. This procedure is of more importance in the case of contact problems, its primary object being to avoid interpenetration. The work was done in the ZATILAN code, developed by the Department of Mechanical Engineering of the University of the Basque Country.

The localized strain softening behaviour of concrete has been modelled by two approaches: (i) the stiffness degrading model based on the total stress‐strain constitutive relationship, and (ii) the tangent softening model based on the incremental stress‐strain relationship. The models are implemented using a new softening initiation criterion proposed for application in multi‐dimensional finite element analysis. Parametric analyses on plain concrete beams, tested experimentally by other researchers, have been carried out to investigate the required numerical efforts, the mesh objectivity, and the energy dissipation characteristics of the structures. The stiffness degrading model is very stable even when applied with relatively coarse finite element meshes. However, the computational demand of this model is relatively high. The combination of a total stress‐strain constitutive relationship to compute the element responses, and an incremental relationship to formulate the stiffness matrix, appears to be computationally efficient and stable, provided that adequately refined finite element mesh is used to model the structure.

Some frictional contact problems are characterized by significant variations in the location and size of the contact area occurring in the process of deformation. When this feature is combined with strongly non‐linear, path‐dependent material behaviour, difficulties with convergence of the typically used iterative processes can be encountered. Demonstrates this by analysis of press‐fit connection, a typical problem in which both of those characteristics can be present. Offers an explanation as to the possible source of those difficulties. Suggests in support of this explanation, two simple modifications of the usual iterative schemes. In spite of their simplicity, they are found to be more robust than those usual schemes which are normally used in numerical analysis of similar problems.

In the inelastic stability analysis of plated structures, incremental‐iterative finite element methods sometimes encounter prohibitive solution difficulties in the vicinity of sharp limit points, branch points and other regions of abrupt non‐linearity. Presents an analysis system that attempts to trace the non‐linear response associated with these types of problems at minor computational cost. Proposes a semi‐heuristic method for automatic load incrementation, termed the adaptive arc‐length procedure. This procedure is capable of detecting abrupt non‐linearities and reducing the increment size prior to encountering iterative convergence difficulties. The adaptive arc‐length method is also capable of increasing the increment size rapidly in regions of near linear response. This strategy, combined with consistent linearization to obtain the updated tangent stiffness matrix in all iterative steps, and with the use of a “minimum residual displacement” constraint on the iterations, is found to be effective in avoiding solution difficulties in many types of severe non‐linear problems. However, additional procedures are necessary to negotiate branch points within the solution path, as well as to ameliorate convergence difficulties in certain situations. Presents a special algorithm, termed the bifurcation processor, which is effective for solving many of these types of problems. Discusses several example solutions to illustrate the performance of the resulting analysis system.

A concrete material model is presented. The model is based on non‐associated plasticity for the pre‐failure and ductile post‐failure regimes and fracture (smeared crack approach) for the brittle post‐failure regime. The implementation of the constitutive model in the 2‐D elements of a general purpose non‐linear incremental finite element code is discussed. Some important numerical features of the implementation are the implicit integration of the stress/strain relation and the use of an efficient symmetric stiffness formulation for the equilibrium iterations.

The purpose of this study is to investigate the post-buckling analysis of functionally graded columns by using three analytical, approximate and numerical methods. A pre-defined function as an initial assumption for the post-buckling path is introduced to solve the differential equation. The finite difference method is used to approximate the lateral deflection of the column based on the differential equation. Moreover, the finite element method is used to derive the tangent stiffness matrix of the column.

The non-linear buckling analysis of functionally graded materials is carried out by using three analytical, finite difference and finite element methods. The elastic deformation and Euler-Bernoulli beam theory are considered to establish the constitutive and kinematics relations, respectively. The governing differential equation of the post-buckling problem is derived through the energy method and the calculus variation.

An incremental iterative solution and the perturbation of the displacement vector at the critical buckling point are performed to determine the post-buckling path. The convergence of the finite element results and the effects of geometric and material characteristics on the post-buckling path are investigated.

The key point of the research is to compare three methods and to detect error sources by considering the derivation process of relations. This comparison shows that a non-incremental solution in the analytical and finite difference methods and an initial assumption in the analytical method lead to an error in results. However, the post-buckling path in the finite element method is traced by the updated tangent stiffness matrix in each load step without any initial limitation.

The purpose of this paper is to present a simplified hybrid modeling (HYMOD) approach which overcomes limitations regarding computational cost and permits the simulation and prediction of the nonlinear inelastic behavior of full-scale RC structures.

The proposed HYMOD formulation was integrated in a research software ReConAn FEA and was numerically studied through the use of different numerical implementations. Then the method was used to model a full-scale two-storey RC building, in an attempt to demonstrate its numerical robustness and efficiency.

The numerical results performed demonstrate the advantages of the proposed hybrid numerical simulation for the prediction of the nonlinear ultimate limit state response of RC structures.

A new numerical modeling method based on finite element method is proposed for simulating accurately and with computational efficiency, the mechanical behavior of RC structures. Currently 3D detailed methods are used to model single structural members or small parts of RC structures. The proposed method overcomes the above constraints.