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Abstract: Harmonic balance (HB) methods allow for rapid computation of time-periodic solutions for nonlinear dynamical systems. We present a filtered high dimensional harmonic balance (HDHB) approach, which operates in the time domain, and provide a framework for implementation into an existing finite element solver. To demonstrate its capabilities, the method is used to solve a set of nonlinear structural dynamics problems related to the field of flapping flight. For each example, the HDHB approach produces accurate steady-state solutions orders of magnitude faster than a traditional time-marching scheme. [Copyright &y& Elsevier]

The objective of this study is to formulate a general 3D material-structural analysis framework for the thermomechanical behavior of steel-concrete structures in a fire environment The proposed analysis framework consists of three sequential modeling parts: fire dynamics simulation, heat transfer analysis, and a thermomechanical stress analysis of the structure. The fast modeling part consists of applying the NIST (National Institute of Standards and Technology) Fire Dynamics Simulator (FDS) where coupled CFD (Computational Fluid Dynamics) with thermodynamics are combined to realistically model the fire progression within the steel-concrete structure. The goal is to generate the spatial-temporal (ST) solution variables (temperature, heat flux) on the surfaces of the structure. The FDS-ST solutions are generated in a discrete form. Continuous FDS-ST approximations are then developed to represent the temperature or heat-flux at any given time or point within the structure. An extensive numerical study is carried out to examine the best ST approximation functions that strike a balance between accuracy and simplicity. The second modeling part consists of a finite-element (FE) transient heat analysis of the structure using the continuous FDS-ST surface variables as prescribed thermal boundary conditions. The third modeling part is a thermomechanical FE structural analysis using both nonlinear material and geometry. The temperature history from the second modeling part is used at all nodal points. The ABAQUS (2003) FE code is used with external user subroutines for the second and third simulation parts in order to describe the specific heat temperature nonlinear dependency that drastically affects the transient thermal solution especially for concrete materials. User subroutines are also developed to apply the continuous FDS-ST surface nodal boundary conditions in the transient heat FE analysis. The proposed modeling framework is applied to predict the temperature and deflection of the well-documented third Cardington fire test. [ABSTRACT FROM AUTHOR]

The elastic response of curved beams subjected to moving vertical loads and dynamic loads is investigated. Incremental dynamic equilibrium equations are derived by using the principle of virtual work. Newmark's step-by-step procedure is adopted to discretise the dynamic equilibrium equations and obtain the time history response. Geometric nonlinearities due to large deflections and rotations are taken into account. A total Lagrangian finite element formulation is developed. The numerical models are compared with the existing analytical solutions and employed to show the effects of geometric nonlinearities as well as the initial curvature on the dynamic behaviour of curved I-beams. It is shown that the geometric nonlinearities are significant even for service loads. The nonlinear behaviour of a curved beam is substantially different from the nonlinear behaviour of a straight beam when the initial curvature is not small. [ABSTRACT FROM AUTHOR]

Biopolymer gels, such as those made out of fibrin or collagen, are widely used in tissue engineering applications and biomedical research. Moreover, fibrin naturally assembles into gels in vivo during wound healing and thrombus formation. The macroscale properties of fibrin and other biopolymer gels are dictated by the response of a microscale fiber network. Hence, accurate description of biopolymer gels can be achieved using representative volume elements (RVE) that explicitly model the discrete fiber networks of the microscale. These RVE models, however, cannot be efficiently used to model the macroscale due to the challenges and computational demands of multiscale coupling. Here, we propose the use of an artificial, fully connected neural network (FCNN) to efficiently capture the behavior of the RVE models. The FCNN was trained on 1100 fiber networks subjected to 121 biaxial deformations. The stress data from the RVE, together with the total energy on the fibers and the condition of incompressibility of the surrounding matrix, were used to determine the derivatives of an unknown strain energy function with respect to the deformation invariants. During training, the loss function was modified to ensure convexity of the strain energy function and symmetry of its Hessian. A general FCNN model was coded into a user material subroutine (UMAT) in the software Abaqus. The UMAT implementation takes in the structure and parameters of an arbitrary FCNN as material parameters from the input file. The inputs to the FCNN include the first two isochoric invariants of the deformation. The FCNN outputs the derivatives of the strain energy with respect to the isochoric invariants. In this work, the FCNN trained on the discrete fiber network data was used in finite element simulations of biopolymer gels using our UMAT. We anticipate that this work will enable further integration of machine learning tools with computational mechanics. It will also improve computational modeling of biological materials characterized by a multiscale structure. [Display omitted] • Multiscale mechanics of biopolymer gels using a machine learning metamodel of discrete fiber networks. • User material subroutine (UMAT) for Abaqus evaluates arbitrary neural networks defined in the input file. • Invariant formulation from Gaussian process regression of the total energy constrained on the stress data. • Loss function enforces strain energy convexity and symmetry of the Hessian. [ABSTRACT FROM AUTHOR]

Three classes of structural models can be considered for the characterization of thin extensible pressurized membranes. A low-fidelity, linear model assumes that all of the membrane’s resistance to a transverse pressure is provided from geometric stress-stiffening, and that movement along the membrane is purely out-of-plane. A medium-fidelity model can include geometric nonlinearity (finite strains, non-conservative pressure loads); while the highest level of membrane modeling assumes material nonlinearity: specifically, hyperelasticity. Common modeling applications such as performance prediction, failure prevention, and structural optimization all require repeated function evaluations. As computational cost is proportional to model fidelity, what is the validity range of the two lower fidelity models discussed above? The presence of a large pre-tension within the membrane is known to lessen the role of nonlinear elastic effects: the range of linear transverse deformation increases with pre-tension. Conversely, very low pre-tensions require the use of a nonlinear model, as the linear model becomes unbounded. This work studies the Hencky–Campbell problem for model validation purposes: hydrostatic inflation of a thin flat circular membrane, clamped along its boundary, with an arbitrary initial tension. A full-field, non-contact visual image correlation system is used to estimate the material properties of the rubber membrane, measure the state of pre-tension in the circular sheet, and document the displacement and strain fields as a function of applied pressure. The resulting data set is then compared directly with numerical simulations, in order to estimate the location of the surface of data points wherein a particular low fidelity model (either linear or geometrically nonlinear) loses its predictive capability. [ABSTRACT FROM AUTHOR]

This paper presents the implementation of Reissner's (J. Appl. Math. Phys. 1972; 23:795–804) strain–displacement relations for a planar beam using a variable order secant matrix (VOSM) technique. The secant matrices are formed using a Taylor expansion of the strain energy and hence the order of the secant and tangent matrices to be included in the nonlinear analysis can be varied depending upon the degree of nonlinearity involved in the problem. Nevertheless, a maximum of 24 matrices is sufficient to obtain predicted internal stress resultants to within 0.2% of the converged solution in all the problems tested. Using a three-noded isoparametric beam element, the accuracy of the VOSM method is demonstrated for the elastic postbuckling of arches. Copyright © 2007 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper describes a functional tool for engineers to make rational design decisions by balancing cost and safety. Focus is on seismic design, in which nonlinear structural response must be considered. For this purpose, we implement and apply a state-of-the-art algorithm for reliability-based design optimization. The work extends the OpenSees software, which is rapidly gaining users in the earthquake engineering community. Consequently, design optimization with sophisticated nonlinear finite element models of real structures is possible. An object-oriented software architecture is employed that focuses on maintainability and extensibility of the software. This approach also offers flexibility in the choice of optimization and reliability methods for each specific problem, supported by the decoupled nature of the optimization algorithm. Our work utilizes and extends the existing tools for structural reliability analysis in OpenSees. In particular, we employ response sensitivities that are computed within the finite element code by direct differentiation. The implementation is tested through case studies with nonlinear structural response. Discontinuous response gradients are overcome by use of fibre cross sections and smoothed material models. The numerical examples include the seismic design optimization of a six-storey, three-bay, reinforced concrete building. [ABSTRACT FROM AUTHOR]

Abstract: A set of nonlinear, intrinsic equations describing the dynamics of beam structures undergoing large deformations is presented. The intrinsic kinematical equations are derived for the general case of a moving beam. Active force/strain terms are added to the equations to take into account active components. The equations are then discretized into finite elements, transformed into state-space form and finally decomposed into modes. Actuation and sensor models are established before implementing a simulation model in Matlab/SIMULINK. The model is validated by comparison with exact, analytical results and then used to analyze the dynamic behavior of an active helicopter blade in vacuum. Beside the analysis of the inherent dynamics of this system in terms of eigenvalues and vectors, the influence of centrifugal stiffening on the modal controllability of the blade is discussed. Finally, the design of a MIMO controller based on full-state optimal control (LQR approach) and optimal state estimation (Kalman filter) is presented with the aim to add vibrational damping to the weakly damped system. The closed loop properties are validated by both analytical methods and simulation runs. [Copyright &y& Elsevier]

Abstract: The helicoidal modeling of the continuum, as proposed in Part I, is applied to finite elasticity analyses of simple materials unable of couple-stressing. First, the non-polar medium is introduced via a constitutive postulate and results in a sort of constrained medium, having the axial vector of the Biot stress tensor as a primary unknown field and the statement of polar decomposition of the deformation gradient as a governing equation. Next, the variational formulation is accommodated to the non-polar case, and the ensuing principle is approximated by the finite element method. The nonlinear finite elements have the nodal oriento-positions as degrees-of-freedom and are based on the multiplicative interpolation developed in Part II. The interpolation and an analysis methodology based on the multiplicative updating of the kinematical unknowns, ensure frame-invariant and path-independent solutions. Several examples, with either linear or nearly incompressible Neo-Hookean elastic materials, attest the performance of the proposed modeling in high deformation problems with large three-dimensional rototranslations. [Copyright &y& Elsevier]

Abstract: This paper presents an elasto-plastic damage model that is based on irreversible thermodynamics and internal state variable formalism for the analysis of multi-layered composites. The model is based on a damage surface that is defined in terms of an internal damage variable of energy, along with a set of rate-independent elasto-plastic constitutive equations defined in an effective stress–strain space. Employing the operator splitting methodology, a three-step predictor/multi-corrector algorithm is developed that includes an elastic predictor, a plastic corrector, and a damage corrector. The constitutive model is cast in a co-rotational kinematic framework for damage analysis in laminated plates and shells undergoing large deflections. Numerical examples are presented to demonstrate the accuracy and range of applicability of the proposed model. [Copyright &y& Elsevier]

Geometrically exact beams are regarded from the outset as constrained mechanical systems. This viewpoint facilitates the discretization in space and time of the underlying continuous beam formulation without using rotational variables. The present semi-discrete beam equations assume the form of differential–algebraic equations which are discretized in time. The resulting energy–momentum scheme satisfies the algebraic constraint equations on both configuration and momentum level. [ABSTRACT FROM AUTHOR]

To produce functional, aesthetically natural results, reconstructive surgeries must be planned to minimize stress as excessive loads near wounds have been shown to produce pathological scarring and other complications (Gurtner et al., 2011). Presently, stress cannot easily be measured in the operating room. Consequently, surgeons rely on intuition and experience (Paul et al., 2016; Buchanan et al., 2016). Predictive computational tools are ideal candidates for surgery planning. Finite element (FE) simulations have shown promise in predicting stress fields on large skin patches and in complex cases, helping to identify potential regions of complication. Unfortunately, these simulations are computationally expensive and deterministic (Lee et al., 2018a). However, running a few, well selected FE simulations allows us to create Gaussian process (GP) surrogate models of local cutaneous flaps that are computationally efficient and able to predict stress and strain for arbitrary material parameters. Here, we create GP surrogates for the advancement, rotation, and transposition flaps. We then use the predictive capability of these surrogates to perform a global sensitivity analysis, ultimately showing that fiber direction has the most significant impact on strain field variations. We then perform an optimization to determine the optimal fiber direction for each flap for three different objectives driven by clinical guidelines (Leedy et al., 2005; Rohrer and Bhatia, 2005). While material properties are not controlled by the surgeon and are actually a source of uncertainty, the surgeon can in fact control the orientation of the flap with respect to the skin's relaxed tension lines, which are associated with the underlying fiber orientation (Borges, 1984). Therefore, fiber direction is the only material parameter that can be optimized clinically. The optimization task relies on the efficiency of the GP surrogates to calculate the expected cost of different strategies when the uncertainty of other material parameters is included. We propose optimal flap orientations for the three cost functions and that can help in reducing stress resulting from the surgery and ultimately reduce complications associated with excessive mechanical loading near wounds. [ABSTRACT FROM AUTHOR]

• Non-intrusive, modal derivatives-based reduced order model developed for geometrically nonlinear vibrations. • The computation of modal derivatives is load-independent. • The method does not require any ad hoc selection of parameters to form the basis. • The Method is checked for random response prediction on three numerical examples. • Accuracy and computational efficiency of the proposed approach are compared with state-of-the-art methods. Non-intrusive model-order reduction methods are beneficial for reducing the computational costs of dynamic analysis of nonlinear finite element models, developed in programs that do not release nonlinear element forces and Jacobians (e.g., commercial software). One of the key aspects for developing a displacement-based non-intrusive reduced order model is a proper construction of the reduction basis, which has to be small in size, easy to compute, and must span the subspace in which the full solution lives. In this paper, we propose a non-intrusive model order reduction method based on modal derivatives stemming from a selected set of vibration modes of the linearized system. By definition, modal derivatives do not require the knowledge of the applied load. We name this load-independent basis. The method we propose is also simulation-free, meaning that no nonlinear dynamic simulations of the full model are required to construct the reduction basis. The method is tested with three examples of increasing complexity. [ABSTRACT FROM AUTHOR]

A new three-dimensional, finite deformation Cosserat continuum model for the elastic response of uncured carbon fibre composites is presented. The new composite process model captures the bending contribution of bundles of fibres at the microscale within a mesoscale continuum description of a composite ply. This is achieved by introducing higher-order, independent rotational degrees of freedom into the continuum formulation. This paper demonstrates the inclusion of such mechanics is essential to accurately model various bending responses induced during typical composite manufacturing processes. This includes large deformation forming, finite strain consolidation and wrinkling (the formation of an unwanted defect). If such mechanics are not included, the literature demonstrates the resulting finite element solutions have a pathological dependence on the mesh size. As a result, simulations require users to fit mesh-dependent material parameters, which limits confidence in their predictive capabilities. The Cosserat continuum, which can be seen as a form of the regularised continuum model, overcomes these challenges. In particular, this paper presents details of the finite element formulation of the new continuum model within a nonlinear Taylor–Hood Cosserat Element. Implementation details of embedding this new element within the commercial code Abaqus are given, alongside a series of increasingly complex validation simulations. Notably, the examples include modelling the formation of internal fibre wrinkles and large deformation forming, which involves complex ply-to-ply and tool-to-ply contact. The paper concludes by describing: (1) how the elastic Cosserat model can be integrated into existing large deformation process models in the literature. The approach set out readily allows researchers to include the important effects of resin flow, cure kinetics and temperature distribution, not considered in this contribution, and (2) how it is envisaged that the ply scale model can be naturally scaled up to large laminate scale simulation using mathematical upscaling techniques. • A three-dimensional, finite deformation Cosserat continuum model for the elastic response of uncured carbon fibre composites is presented. • The proposed composite process model captures the bending contribution of bundles of fibres at within the continuum description of a composite ply through introducing higher-order, independent rotational degrees of freedom. • The finite element formulation of a new nonlinear Taylor-Hood Cosserat Element and the implementation details of this new element within the commercial code ABAQUS are presented. • The new finite deformation Cosserat model for composite processing modelling is demonstrated, parametrised and validated with four relevant case studies. [ABSTRACT FROM AUTHOR]

This paper presents a consistent corotational formulation for the geometric nonlinear dynamic analysis of 2D sliding beams. Compared with the works of previously published papers, the same cubic shape functions are used to derive the elastic force vector and the inertia force vector. Consequently, the consistency of the element is ensured. The shape functions are used to describe the local displacements to establish an element-independent framework. Moreover, all kinds of standard elements can be embedded within this framework. Therefore, the presented method is more versatile than previous approaches. To consider the shear deformation, the sliding beam (a system of changing mass) is discretized using a fixed number of variable-domain interdependent interpolation elements (IIE). In addition, the nonlinear axial strain and the rotary inertia are also considered in this paper. The nonlinear motion equations are derived by using the extended Hamilton's principle and solved by combining the Newton-Raphson method and the Hilber-Hughes-Taylor (HHT) method. Furthermore, the closed-form expressions of the iterative tangent matrix and the residual force vector are obtained. Three classic examples are given to verify the high accuracy and efficiency of this formulation by comparing the results with those of commercial software and published papers. The simulation results also show that the shear deformation and the rotary inertia cannot be neglected for the large-rotation and high-frequency problem. [ABSTRACT FROM AUTHOR]

During the disassembly phase of the refurbishment of the National Institute of Standards and Technology 4.45 MN Deadweight Machine, workers confirmed previously suspected damage in certain conical contact joints within the apparatus. A finite element analysis of the contact joints is performed with the aim of understanding some of the potential origins of failure in order to prevent future damage in the machine. Parametric studies are performed using a finite element model while varying geometry, material constitutive relations, and frictional forces at the interface of the convex and concave cones. The numerical solutions treat nonlinearities originating from elastic-plastic material relations, frictional forces, and contact between the surfaces. These results provide insights into the mechanisms of stress generation in such joints, and how these stresses are influenced by different structural parameters.