CALEB: A COMPUTER PROGRAM FOR GEOMETRICAND MATERIAL NONLINEAR ANALYSIS OFOFFSHORE PLATFORMS AND GENERAL FRAMEDSTRUCTURES

A comparative study of shape imperfection and internal pressure effects on plastic, shakedown and elastic limit loads using large and small strain formulation of 90° pipe bends

An energy balancing strategy for solution of combined geometrical and material nonlinearity problems

Nonlinear structural analysis, which can account for geometrical or material nonlinearities beyond the scope of linear methods, typically incurs high computational costs. Recent advances have shown that quantum computers can accelerate various numerical simulations. Although quantum acceleration of linear structural analysis via the Quantum Linear System Algorithm (QLSA) has been studied, its application to nonlinear structural analysis remains unexplored. Here, we introduce our proposed quantum algorithm for accelerating nonlinear structural analysis, summarizing its key features and performance results from our recent study.

An analysis is described that models the behavior of planar prestressed concrete cable‐stayed bridges up to failure taking into account geometric and material nonlinearities. The geometric nonlinearities arise from cable sag, large deformations of the system, and from the shift of the centroid of the deck section caused by the material or by cracking of the concrete. The effect of the axial forces on the stiffness of the members is also considered. Material nonlinearities are encountered when one or more of the structure components, namely the stay cables, prestressing tendons, the reinforcement, or the concrete, exceed their elastic limits. Parametric studies are made on cable‐stayed bridges with the following cable arrangements: fan, semifan and harp‐type cable arrangement. To demonstrate the influence of the different types of nonlinearity on the internal forces and reactions three analyses were performed—namely elastic, geometric nonlinear, and geometric and material nonlinear analyses—and the results...

Abstract. In this study, we employ low and high-fidelity finite beam elements to conduct geometrical nonlinear transient analyses of composite and sandwich structures. The equations of motion for various structural theories are derived in a total Lagrangian scenario using the Carrera Unified Formulation. The unified formalism's three-dimensional nature enables us to include all components of the Green-Lagrange strain tensor. To solve the equations, we utilize the Hilber-Hughes-Taylor (HHT)-α algorithm in conjunction with a Newton-Raphson procedure. We present the dynamic response of a sandwich stubby beam subjected to a step load, calculated using both equivalent-single layer and layer-wise approaches. Additionally, we discuss the effects of geometrical nonlinearity.

Geometrical nonlinearity arises from the continuous change of shape under increasing loads on thin or long span members, and the materials nonlinearity due to the nonlinear behavior of the materials composing the structural element. In this study the finite element method is used to analyze fibrous reinforced concrete slabs, material and geometric nonlinearities were considered. Concrete is represented by degenerate quadratic thick shell element. Concrete behavior in compression is modeled by elastic perfectly plastic or strain hardening plasticity. A tensile strength criterion is used to follow crack initiation and propagation. A parabolic stress degradation function, which is based on the fracture energy concept, is used to model the tension stiffening effect of steel fibers. The reinforcement is considered as smeared within the concrete layers, and assumed as either an elastic perfectly plastic material or as an elastic-plastic material with linear strain hardening. Von Karman assumptions which is based on the total Lagrangian approach is used for the geometric nonlinearity. The numerical results using for both normal and lightweight fiber reinforced concrete slabs were predicted satisfactorily. The average predicted failure load of the investigated cases to the experimental failure load was 0.899 with a standard deviation of 0.092.

A novel approach for seismic nonlinear analysis of inelastic framed structures is presented in this paper. The nonlinear analysis refers to the evaluation of structural response considering P -delta effect, which is in the form of geometric nonlinearity, and inelastic behavior refers to material nonlinearity. This novel approach uses finite element formulation to derive the elemental stiffness matrices, particularly to derive the geometric stiffness matrix in a general form. At the same time, this approach separates the inelastic displacement from total deflection of the structure by applying two additional constant matrices, namely, the force–recovery matrix and the moment-restoring matrix in the force analogy method. The benefit behind this treatment is explicitly locating and calculating the inelastic response, together with strategically separating the coupling effect between the material nonlinearity and geometric nonlinearity, during the time history analysis. Comparison with the traditional increme...

PurposeThis paper aims to present development of a layer‐wise (LW) beam model for geometric nonlinear finite element analysis of laminated beams with partial layer interaction.Design/methodology/approachThe model is built assuming first order shear deformation theory (FSDT) at layer level and moderate interlayer slips. LW kinematic, strain and stress fields are established in view of co‐rotational finite element formulation. Laminated beam equilibrium relations are developed in strong, weak and matrix form. A notion of interface shear stress is used to define layer interactions.FindingsThrough suitable choice of kinematic model the co‐rotational approach is shown to provide means of obtaining robust finite element formulation for geometric nonlinear analysis of laminated structures with interlayer slips.Research limitations/implicationsThe proposed model is dedicated to geometric nonlinear finite element analysis of laminated beams undergoing large planar displacements, subject to small strains and moderate interlayer slips.Originality/valueNovelty of the proposed approach is based on encompassing shear deformations in geometric nonlinear analysis of laminated beams with interlayer slips. Arbitrary number of layers is considered.

Given the vast advancements in computing power in the last several decades, nonlinear dynamic analysis has gained wide acceptance by practicing engineers as a useful way of assessing and improving the seismic performance of structures. Nonlinear structural analysis software packages give engineers the ability to directly model nonlinear component behavior in detail, resulting in improved understanding of how a building will respond under strong earthquake shaking. One key component, in particular, for understanding the behavior of moment-resisting frames is the plastic rotation of the flexural hinges. Performance-based standards typically use plastic rotation as the primary parameter for defining the acceptance criteria in moment-resisting frames. Since plastic rotation is a key parameter in the seismic damage assessment, the concept as well as the method to calculate this quantity must be understood completely. Though engineers rely on the plastic rotation output from seismic structural analysis software packages to determine acceptable performance, the actual calculation methods used in achieving such plastic rotation quantities usually lay within a so-called “black box”. Based on the outputs obtained from most structural analysis software packages, it can be shown that running an algorithm considering material nonlinearity by itself will produce reasonably accurate results. Moreover, separately running an algorithm considering geometric nonlinearity also can produce accurate results. However, when material nonlinearity is combined with geometric nonlinearity in an analysis, obtaining accurate results or even stable solutions is more difficult. The coupling effect between the two nonlinearities can significantly affect the global response and the local plastic rotation obtained from the analysis and therefore needs to be verified through some analytical means. Yet, the verification process is difficult because a robust analytical framework for calculating plastic rotation is currently unavailable and urgently needed. In view of this gap, an improved analytical approach based on small displacement theory is derived to calculate the plastic rotations of plastic hinges at various locations of moment-resisting frames. Both static and dynamic analysis with nonlinear geometric effects will be incorporated in the derivation. Here the element stiffness matrices are first rigorously derived using a member with plastic hinges in compression, and therefore the coupling of geometric and material nonlinearity effects is included from the beginning of the derivation. Additionally, plastic rotation is handled explicitly by considering this rotation as an additional nonlinear degree-of-freedom. Numerical simulation is performed to calculate the nonlinear static and dynamic responses of simple benchmark models subjected to seismic excitations. Results are compared with various software packages to demonstrate the feasibility of the proposed method in light of the output results among software packages in calculating plastic rotations.

Adhesive joints serve under thermal loads as well as structural loads. The different thermo-mechanical properties of the adhesive and adherend materials cause incompatible thermal strains along the adhesive and adherend interfaces. Consequently, nonuniform thermal stress distributions are observed in the adhesive joints. In case the adhesive joints are constrained, these thermal stresses become more evident even for a uniform temperature distribution. In practice the adhesive joints interact with fluids (air) with different temperature and velocity and experience conductive and convective heat transfers. The variable thermal boundary conditions introduce a new non-linearity in addition to the geometrical and material non-linearities which are observed in adhesive joints. The transient temperature distributions can be obtained by solving the energy equation under the thermal boundary conditions. The corresponding thermal strain and stress distributions can be calculated using the transient temperature distributions. The large displacement and rotations occurring in adhesive joints require the implementation of the small strain-large displacement theory to the elastic stress analysis. This study introduces a simple method for calculating the heat transfer coefficients between the fluid and adhesive joints and explains the implementation of the finite element method to the thermal analysis and the geometrical nonlinear stress analysis. The thermal stresses in the metal-metal adhesive single lap, tubular, metal-metal and composite tee joints were analysed for the variable thermal and specified structural boundary conditions. The variable thermal boundary conditions cause non-uniform temperature distributions through the adhesive lap joints; consequently, non-uniform thermal strain and stress distributions occur. The adherend and adhesive regions in the neighborhood of the adhesive-adherend interfaces were subjected to high stress concentrations.

A formulation of the nonlinear FEM truss element that takes into account both the geometric nonlinearity and material nonlinearity of the structure is derived. The associated iterative algorithm for the application is described. Based on two inelastic material models (isotropic hardening and dynamic hardening), three space truss structures are subjected to static and to dynamic loads in order to illustrate the application of nonlinear FEM. The nonlinear FEM described can accurately trace the complex structural behavior of space truss structures, including snap-through, and buckling. The FEM results match well with the theoretical results.

This paper presents a computationally efficient numerical model for the analysis of thin shells based on rotation-free triangular finite elements. The geometry of the structure in the vicinity of the observed triangular element is approximated through a controlled domain consisting of nodes of the observed finite element and nodes of three adjacent finite elements between which a second-order spatial polynomial is defined. The model considers large displacements, large rotations, small strains, and material and geometrical nonlinearity. Material nonlinearity is implemented by considering the von Mises yield criterion and the Levi–Mises flow rule. The model uses an explicit time integration scheme to integrate motion equations but an implicit radial returning algorithm to compute the plastic strain at the end of each time step. The presented numerical model has been embedded in the program Y based on the finite–discrete element method and tested on simple examples. The advantage of the presented numerical model is displayed through a series of analyses where the obtained results are compared with other results presented in the literature.

Wind resistant size optimization of geometrically nonlinear lattice structures using a modified optimality criterion method

A reliable numerical procedure is proposed for the geometric nonlinear dynamic analysis of suspension bridges subjected to earthquake excitations. The geometric nonlinearities of cable members are captured by the catenary element derived from exact analytical expressions of elastic catenary, while the geometric nonlinearities of tower and girder members are predicted by nonlinear beam element which can undergo large deflections and rotations. An incremental-iterative solution based on Newmark-β direct integration and Newton–Raphson iteration is adopted for solving the nonlinear equation of motion. The results are compared with those generated by ANSYS to show the accuracy and efficiency of the proposed procedure.

Owing to their low induced drag, high-aspect-ratio wings are often applied to aircraft, particularly high-altitude long-endurance (HALE) aircraft. An analytical method that considers geometrical nonlinearity is necessary for the analysis of high-aspect-ratio wings as they tend to undergo large deformations. Nonlinear shell/plate or solid finite element methods are widely used for the static analysis of wing strength. However, an increase in the number of elements drastically increases the computational costs owing to the complexity of wing shapes. The modal rotation method (MRM) can avoid this additional expense by analyzing large deformations based on modes and stiffness matrices obtained from any linear or linearized model. However, MRM has only been formulated as a static analysis method. In this study, a novel modal-based dynamic analysis framework, referred to as dynamic MRM (DMRM), is developed to analyze slender cantilever structures. This paper proposes a method to discretize dynamics by capitalizing on the fact that MRM considers geometrical nonlinearity based on deformed shapes. The proposed method targets slender structures with small strains and large displacements and considers geometrical nonlinearity, but not material nonlinearity. Additionally, a formulation method for the work performed by a follower force is proposed. The energy stored in the structure agreed with the work performed by an external force in each performed simulation. DMRM achieved a 95% reduction in the calculation time compared with a nonlinear plate finite element method in a performed simulation.