Solid-shell Finite Element Model Research Articles

Stress Analysis and Structural Optimization of Steel–Concrete Joint of Zhonghua Road Bridge in Liaocheng

Based on Zhonghua Road Bridge in Liaocheng city, a single tower hybrid cable-stayed bridge, the stress of the steelconcrete joint of the girder is studied using the finite element method with the software MIDAS and ANSYS. The beam element model of the whole bridge is established in MIDAS CIVIL, from which the internal forces of the critical sections of the steel–concrete joint under six adverse conditions are obtained. Then, the results are applied in the refined solid-shell finite element model established in ANSYS. With the stress analysis, it is found that when the steel–concrete joint is used in the girder of the single tower cable-stayed bridge, both the compressive strength of concrete and the tensile strength of steel can be fully used, and the structural stiffness can be smoothly transferred through the two different materials in the joint, which makes the structural behavior more reasonable. The detailed stress analysis also shows that it is prone to generate considerable stress concentration at the corners and the connection between the steel lattice chamber and the pressure bearing plate, and the concentration can be avoided by local stiffening and smoothing of the chamfers. The sensitivity analysis of the web thickness in the joints and bearing plates showed that increasing the thickness of the intermediate web would lead to a moderate reduction in the stress of the web itself, while the stress in the steel member remained relatively constant. However, when the thickness of the bearing plate is increased from 60 to 80 mm, the stress of each part of the steel plate in the steel grid will be significantly reduced, and the maximum reduction can reach 48%. The improvement of concrete strength has little effect on the stress of the steel cell, and the C50 concrete strength grade used in the design is more reasonable.

A constrained solid-shell model for the geometric nonlinear finite-element analysis of laminates with alternating stiff/soft layers. Applications to laminated glass

Solid-shell models are developed for the geometrically nonlinear analysis of multi-layered composite structures made of alternating layers with large difference in material properties. Exemplificative applications are presented for laminated glass, in which a number of stiff plies of glass are permanently shear-coupled by soft interlayers. The sectional warping due to significant transverse shear strains in the soft layers makes theories of laminated plates based on the plane-section hypothesis unreliable. The proposed approach is based on a geometrically exact solid-shell finite element model with one element per layer in the thickness direction, as alternative to solid discretization. The element approximation is based on the displacement nodal values at the top and bottom surfaces of the layers, with a natural C0 continuity. An alternative solid-shell model with fewer parameters is derived imposing the equal finite rotation of the stiff layers at each surface point by a local rotation-free re-parametrization of the nodal displacements and enforcing the plane stress condition. The approach permits an easy coupling with a fully solid discretization, e.g. to model connections, and is based on a simple strain measure quadratic in the displacement unknowns and suitable for finite strains. Extensive numerical examples for laminated glass plates and curved shells susceptible to large deflections and buckling are provided, comparing the results with those from a fully solid approach.

Numerical study on the fire behaviour of restrained steel-concrete composite beams

An elaborate solid-shell finite element model was developed to investigate the fire behavior of restrained steel-concrete composite beams. The model was validated against experimental results in literatures. Parametric studies were also performed to study the parameters including restraint stiffness, load ratio, span, exposure length, embedding depth, steel beam height and protective layer on the fire behavior of restrained composite beam. The analysis results show that the mechanical response of restrained composite beams goes through four phases: elastic, elasto-plastic, rapid plastic deformation and plastic catenary action phase. With the decrease of restraint stiffness, the increase of load and span, the failure mode of the restrained composite beam changes from overall lateral instability to a sharp increase in deformation rate, and the code BS476-20 and ISO834 underestimate the fire resistance of restrained composite beams. The negative bending moment at the beam end increases sharply and reaches the peak value within a short fire time. Therefore, reinforcement shall be provided at the top of the concrete slab near the support section. Furthermore, the difference in fire resistance of restrained composite beams is mainly reflected in the plastic catenary action phase. When the load ratio is less than 0.5, the fire resistance of restrained composite beams can be improved by reducing the fire range, beam height and span, and increasing the axial restraint stiffness. When the load ratio is 0.7, the fire resistance of restrained composite beam is hardly affected by the axial restraint stiffness and span, while with the exposure length reducing from 5 m to 4 m, embedded depth increasing from 0 mm to 50 mm, and the protective layer increasing from 0 mm to 10 mm, the fire resistance of the composite beams increases by 114 min and 160 min and 76 min, respectively.

Prediction of Load-Bearing Capacity of Composite Parts with Low-Velocity Impact Damage: Identification of Intra- and Inter-Ply Constitutive Models

Assessments of residual load-carrying capacity are often conducted for composite structural components that have received impact damage. The availability of a verified simulation methodology can provide significant cost savings when such assessments are required. To support the development of a reliable and accurate simulation methodology, this study investigated the predictive capabilities of a stacked solid-shell finite element model of a cylindrical composite component with a damage mechanics-based description of the intra-ply material response and a cohesive contact model used for simulation of the inter-ply behavior. Identification of material properties for the model was conducted through mechanical characterization. Special attention was paid to understanding the influence of non-physical parameters of the intra- and inter-ply material models on predicting compressive failure load of damaged composite cylinders. Calibration of the model conducted using the response surface methodology allowed for identifying rational values of the non-physical parameters. The results of simulations with the identified and calibrated finite element model showed reasonable correlation with experimental data in terms of the predicted failure loads and post-impact and post-failure damage modes. The investigated modeling technique can be recommended for evaluating the residual load-bearing capacity of flat and curved composite parts with impact damage working under the action of compressive loads.

Structural gradient based sizing optimization of wind turbine blades with fixed outer geometry

In this work the mass of a 73.5 m offshore wind turbine blade is minimized while considering manufacturing constraints, tip displacement, buckling, and static strength criteria when subject to an extreme load envelope consisting of 12 load directions. The gradient based sizing optimization takes offset in the outer geometry and loading from a commercial 73.5 m wind turbine blade where the manufacturing mold should be re-used and hence the outer geometry is kept constant. A solid-shell finite element model of the full blade is used as basis for the optimization. The blade is divided into patches and thicknesses of ply-groups (groups of contiguous plies with the same material and fiber orientation) are used as design variables. The design variables are assumed continuous in the optimization phase. Sequential linear programming (SLP) is used to solve the problem with semi-analytical gradients. In the post-processing phase the lay-up is refined and ply-group thicknesses are rounded to a whole number of plies. The gradient based sizing optimization results in a reduced mass and many active constraints across multiple load directions while the post-processing ensures manufacturability.

Post-buckling optimisation strategy of imperfection sensitive composite shells using Koiter method and Monte Carlo simulation

A numerical stochastic strategy for optimising composite elastic shells undergoing buckling is presented. Its scope is to search for the best stacking sequence that maximises the collapse load considering the post-buckling behaviour. Its feasibility is due to a reduced order model built for each material setup starting from a hybrid solid-shell finite element model exploiting a multimodal Koiter method. The approach has no limitations concerning geometry, boundary conditions and material properties distribution. The collapse load is evaluated using a Monte Carlo simulation able to detect the worst imperfection shape, including a posteriori the imperfections in the reduced order model. For a limited number of parameters the proposal allows to analyse all the possible layups. In the general case, it uses a Monte Carlo scanning of the design parameters with different levels of adaptability. The optimisation of curved panels, also with stiffeners, confirms the feasibility and reliability of the proposed strategy.

Koiter asymptotic analysis of multilayered composite structures using mixed solid-shell finite elements

In this paper we propose a powerful tool for the evaluation of the initial post-buckling behavior of multi-layered composite shells and beams in both bifurcation and limit load cases, including mode interaction and imperfection sensitivity. This tool, based on the joint use of a specialized Koiter asymptotic method and a mixed solid-shell finite element model, is accurate, simple and characterized by a computational cost far lower than standard path-following approaches and many advantages with respect to asymptotic analysis performed with shell elements. The method is very simple and easy to include in existing FE codes because it is based on the same ingredients of a linearized buckling analysis, with very light formula due to the presence of displacement degrees of freedom only. Due to its efficiency it is suitable for layup design when geometrical nonlinearities have to be considered.

Explicit dynamics simulation of blade cutting of thin elastoplastic shells using “directional” cohesive elements in solid-shell finite element models

The intentional or accidental cutting of thin shell structures by means of a sharp object is of interest in many engineering applications. The process of cutting involves several types of nonlinearities, such as large deformations, contact, crack propagation and, in the case of laminated shells, delamination. In addition to these, a special difficulty is represented by the blade sharpness, whose accurate geometric resolution would require meshes with characteristic size of the order of the blade curvature radius. A computational finite element approach for the simulation of blade cutting of thin shells is proposed and discussed. The approach is developed in an explicit dynamics framework. Solid-shell elements are used for the discretization, in view of possible future inclusion in the model of delamination processes. Since a sharp blade can interfere with the transmission of cohesive forces between the crack flanks in the cohesive process zone, standard cohesive interface elements are not suited for the simulation of this type of problems unless extremely fine meshes, with characteristic size comparable to the blade curvature radius, are used. To circumvent the problem, the use of a new type of directional cohesive interface element, previously proposed for the simulation of crack propagation in elastic shells, is further developed and reformulated for application to the cutting of elastoplastic thin structures, discretized by solid-shell elements. The proposed approach is validated by means of application to several cutting problems of engineering interest.

On the modeling and design of composite multilayered structures using solid-shell finite element model

In this investigation a coupling between a 3D solid-shell element for the analysis of multilayered composite shell structures and a specific response surface method is proposed. The first part of the paper is dedicated to the finite element formulation of a developed composite 8-node solid-shell element called SCH8γ7, based only on translational degrees of freedom. The basis of the present finite element formulation is the standard 8-node brick element with tri-linear shape functions. A particular attention is given to alleviate shear, trapezoidal and thickness locking, without resorting to the classical plane-stress assumption. Assumed natural strain method and enhanced assumed strain method are used to improve the relative poor element behavior of a standard hexahedral displacement element. The anisotropic material behavior of layered shells is modeled using a fully three dimensional elastic orthotropic material law in each layer, including the thickness stress component. The second part of the paper will focus on an adaptive response surface method for the structural optimization problem. The response surfaces are built using moving least squares approximations and design of experiments by means of a specific method called Diffuse Approximation.Several numerical applications to composite multilayered shell structures are studied to show the applicability and effectiveness of the proposed procedure. Good results of analysis and optimization using the developed SCH8γ7 solid-shell element have been obtained in comparison with reference analytical solutions and with those obtained using the SC8R solid-shell finite element available in ABAQUS© code.

Development and validation of a subject-specific finite element model of a human clavicle

This study aimed to develop and validate a finite element (FE) model of a human clavicle which can predict the structural response and bone fractures under both axial compression and anterior–posterior three-point bending loads. Quasi-static non-injurious axial compression and three-point bending tests were first conducted on a male clavicle followed by a dynamic three-point bending test to fracture. Then, two types of FE models of the clavicle were developed using bone material properties which were set to vary with the computed tomography image density of the bone. A volumetric solid FE model comprised solely of hexahedral elements was first developed. A solid-shell FE model was then created which modelled the trabecular bone as hexahedral elements and the cortical bone as quadrilateral shell elements. Finally, simulations were carried out using these models to evaluate the influence of variations in cortical thickness, mesh density, bone material properties and modelling approach on the biomechanical responses of the clavicle, compared with experimental data. The FE results indicate that the inclusion of density-based bone material properties can provide a more accurate reproduction of the force–displacement response and bone fracture timing than a model with uniform bone material properties. Inclusion of a variable cortical thickness distribution also slightly improves the ability of the model to predict the experimental response. The methods developed in this study will be useful for creating subject-specific FE models to better understand the biomechanics and injury mechanism of the clavicle.

The simulation of sheet metal forming processes via integrating solid-shell element with explicit finite element method

Solid-shell elements can be seen as a class of typical double-surfaced shell elements with no rational degrees of freedom, which are more suitable for analyzing double-sided contact problems than conventional shell elements. In this study, a solid-shell finite element model is implemented into the explicit finite element software ABAQUS/Explicit as a user-defined element, through which the sheet metal forming processes are simulated. The main feature of this finite element model is that the solid-shell element formulation is embedded into an explicit finite element procedure, compared to the previous studies on the solid-shell elements under the implicit finite element framework. To obtain a straightforward element, a complete integration scheme is adopted. No loss of generality, a twelve-parameter enhance assumed strain method is employed to improve the element’s behavior. Two benchmarks from the NUMISHEET conference and a U-channel roll-forming process are simulated with this explicit solid-shell finite element model. The calculated results are comparable with experimental and numerical results presented in the literatures.

Fabric drape simulation by solid-shell finite element method

In the last decade, considerable effort has been channeled into the development of solid-shell finite element models in which there are only translational but no rotational nodal dofs. Comparing with other shell elements, a distinctive advantage of solid-shell elements is that the complication on handling finite rotations does not exist. On the other hand, fabric drape is a typical geometric nonlinear problem in which the problem domain undergoes large displacement and rotation. To date, computational models for drape simulation are mainly grid-based and fe-based. The former models are probably more successful and examples with extensive folds have seldom been reported by using the latter models. In this paper, a bilinear stress-resultant solid-shell element with assumed natural transverse shear and thickness strains is employed for drape analyses. To reduce the computational burden of interpolating the assumed strain field, the solid-shell element is partitioned into a surface, four line and four point sub-elements. The partitioned element is compared with the original elements by popular geometric nonlinear benchmark problems of shells, no practical difference can be noted in both the converged solution and the convergent rate. However, when the elements are applied to drape analyses with long free-hanging length, some nodal directors are often reversed and, thus, the converged solutions are non-physical. The cause has been traced and remedy is devised. Lastly, a number of drape problems with large free-hanging lengths, extensive folds and fabric-to-solid contact are successfully attempted. The predicted views appear to be natural and pleasant.

An Electric Node Concept for Solid-Shell Elements for Laminate Composite Piezoelectric Structures

The eight-node solid-shell finite element models have been developed for the analysis of laminated composite plate/shell structures embedded with piezoelectric actuators and sensors. To resolve the locking problems of the solid-shell elements in laminated materials and improve accuracy, the assumed natural strain method and hybrid stress method are employed. Introduction of the concept of the electric nodes can effectively eliminate the burden of constraining the equality of the electric potential for the nodes lying on the same electrode. Furthermore, the nonlinear electric potential distribution in piezoelectric layer is described by introducing internal electric potential. The developed finite element models, especially electric potential node model, are simpler over other models but can still obtain same accuracy as exact solution described. Several examples are studied and compared with exact solution and other predicted results to illustrate the accuracy of the present model, and efficacy and effect caused by nonlinear electric potential distribution on frequency and electric fields in smart structure modeling.

A hybrid stress ANS solid-shell element and its generalization for smart structure modelling. Part I?solid-shell element formulation

In the recent years, solid-shell finite element models which possess no rotational degrees of freedom and applicable to thin plate/shell analyses have attracted considerable attention. Development of these elements are not straightforward. Shear, membrane, trapezoidal, thickness and dilatational lockings must been visioned. In this part of this paper, a novel eight-node solid-shell element is proposed. To resolve the shear and trapezoidal lockings, the assumed natural strain (ANS) method is resorted to. The hybrid-stress formulation is employed to rectify the thickness and dilatational locking. The element is computationally more efficient than the conventional hybrid elements by adopting orthogonal-assumed stress modes and enforcing admissible sparsity in the flexibility matrix. Popular benchmark tests are exercised to illustrate the efficacy of the elements. In Part II of the paper, the element will be generalized for smart structure modelling by including the piezoelectric effect. Copyright © 2000 John Wiley & Sons, Ltd.