Geometric Nonlinear Analysis Research Articles

Geometrical nonlinear analysis based on optimization technique

• Two triangular shapes are used to formulate the iteration procedure required for nonlinear analysis. • The areas of these shapes are considered as two variables objective functions. • These functions are minimized with respect to each variable. • Two new constraint equations are obtained, which can be utilized for the nonlinear solver. • All of numerical experiences clearly demonstrate the merits of the authors' formulations. In this paper, two triangular shapes are used to formulate iteration procedures required for nonlinear analysis. These triangles are formed by the structural load–displacement curve. The areas of these shapes are considered as two variables objective functions. To find the optimal solutions, these functions are minimized with respect to each variable. As a result, two new constraint equations are obtained, which can be utilized as the nonlinear solver. To demonstrate the merit of authors’ scheme, some geometric nonlinear analyses of shells, frames and trusses are performed. Furthermore, present formulations are compared with the cylindrical arc-length method.

Geometrical nonlinear analysis by plane quadrilateral element

Various corotational schemes for solid, shell, bending plate and beam elements have been proposed so far. Nevertheless, this approach has rarely been utilized for membrane problems. In this paper, a new quadrilateral element will be suggested for solving nonlinear membranes. The simplicity, rapid convergence and high accuracy of the formulation are the three main characteristics of the presented element. It is worth emphasizing; the recommended element can solve structures with irregular geometry and distorted mesh. This element is insensitive to the aspect ratio. In addition, using this element leads to high-accuracy results. Several numerical examples will be tested to prove the high precision of authors' element in coarse distorted meshes with a large aspect ratio.

Nonlinear analysis and optimal design of a novel piezoelectric-driven compliant microgripper

In a piezoelectric-driven microgripper, obtaining parallel grasping and enlarging grasping stroke are important. This paper presents the nonlinear analysis and optimal design of a novel orthogonal displacement amplification mechanism (DAM)-based piezoelectric-driven microgripper without using traditional bridge-type mechanism or multi-stages DAM, which realizes parallel grasping and displacement amplification simultaneously in compact configuration and benefits further miniaturization. The structural design of proposed microgripper is given, in which a novel orthogonal DAM is used as the intermediate mechanism. The geometrical nonlinearity analysis of novel orthogonal DAM is conducted, including the finite difference-based analysis, the variance-based global sensitivity analysis and the correlation analysis. Based on the nonlinear analysis results, a static constraint restricting the large deflection geometrical nonlinearity degree is established. An optimal design framework of the proposed microgripper is further formulated, which maximizes the grasping movements with considering the property of piezoelectric stack actuator, the nonlinear geometric constraints, the established static constraints as well as the dynamic constraint. A design example verifies the optimal design framework, which can reduce the negative effect of large deflection nonlinearity on the orthogonal movement transformation without requiring specific experience. Experimental tests are used to verify the parallel grasping and the displacement amplification of microgripper.

A Review on Stress and Deformation Analysis of Curved Beams under Large Deflection

The paper presents a review on large deflection behavior of curved beams, as manifested through the responses under static loading. The term large deflection behavior refers to the inherent nonlinearity present in the analysis of such beam system response. The analysis leads to the field of geometric nonlinearity, in which equation of equilibrium is generally written in deformed configuration. Hence the domain of large deflection analysis treats beam of any initial configuration as curved beam. The term curved designates the geometry of center line of beam, distinguishing it from the usual straight or circular arc configuration. Different methods adopted by researchers, to analyze large deflection behavior of beam bending, have been taken into consideration. The methods have been categorized based on their application in various formats of problems. The nonlinear response of a beam under static loading is also a function of different parameters of the particular problem. These include boundary condition, loading pattern, initial geometry of the beam, etc. In addition, another class of nonlinearity is commonly encountered in structural analysis, which is associated with nonlinear stress-strain relations and known as material nonlinearity. However the present paper mainly focuses on geometric nonlinear analysis of beam, and analysis associated with nonlinear material behavior is covered briefly as it belongs to another class of study. Research works on bifurcation instability and vibration responses of curved beams under large deflection is also excluded from the scope of the present review paper.

Optimal design of compliant mechanisms using functionally graded materials

This research applies topology optimization to create feasible functionally graded compliant mechanism designs with the aim of improving structural performance compared to traditional homogeneous compliant mechanism designs. Converged functionally graded designs will also be compared with two-material compliant mechanism designs. Structural performance is assessed with respect to mechanical/geometric advantage and stress distributions. Two design problems are presented – a gripper and a mechanical inverter. A novel modified solid isotropic material with penalization (SIMP) method is introduced for representing local element material properties in functionally graded structures. The method of moving asymptotes (MMA) is used in conjunction with adjoint sensitivity analysis to find the optimal distribution of material properties. Geometric non-linear analysis is used to solve the mechanics problem based on the Neo-Hookean model for hyperelastic materials. Functionally graded materials (FGMs) have material properties that vary based on spatial position. Here, FGMs are implemented using two different resource constraints – one on the mechanism’s volume and the other on the integral of the Young’s modulus distribution throughout the design domain. Tensile tests are performed to obtain the material properties used in the analysis. Results suggest that FGMs can achieve the desired improvements in mechanical/geometric advantage when compared to both homogeneous and two-material mechanisms.

A Review on Stress and Deformation Analysis of Curved Beams under Large Deflection

The paper presents a review on large deflection behavior of curved beams, as manifested through the responses under static loading. The term large deflection behavior refers to the inherent nonlinearity present in the analysis of such beam system response. The analysis leads to the field of geometric nonlinearity, in which equation of equilibrium is generally written in deformed configuration. Hence the domain of large deflection analysis treats beam of any initial configuration as curved beam. The term curved designates the geometry of center line of beam, distinguishing it from the usual straight or circular arc configuration. Different methods adopted by researchers, to analyze large deflection behavior of beam bending, have been taken into consideration. The methods have been categorized based on their application in various formats of problems. The nonlinear response of a beam under static loading is also a function of different parameters of the particular problem. These include boundary condition, loading pattern, initial geometry of the beam, etc. In addition, another class of nonlinearity is commonly encountered in structural analysis, which is associated with nonlinear stress-strain relations and known as material nonlinearity. However the present paper mainly focuses on geometric nonlinear analysis of beam, and analysis associated with nonlinear material behavior is covered briefly as it belongs to another class of study. Research works on bifurcation instability and vibration responses of curved beams under large deflection is also excluded from the scope of the present review paper.

Rectangular Gusset Plate Behaviour in Cold-Formed I-Type Steel Connections

Abstract Cold-formed structure connections utilizing gusset plates are usually semi-rigid. This paper investigates the behaviours of rectangular gusset plates in cold-formed connections of elements whose columns and beams are made with lipped back-to-back C-sections. Methods of calculating strength and stiffness are necessary for such semi-rigid joints. The main task of this paper is to determine a method capable of calculating these characteristics. The proposed analytical method could then be easily adapted to the component method that is described in part 1993-1-8 of the Eurocode. This method allows us to calculate both the strength and stiffness of rectangular gusset plates, assuming that the joint deforms only in plane. This method of design moment resistance calculation was presented taking into account that an entire cross-section shall reach its yield stress. A technique of stiffness calculation was presented investigating the sum of deformations acquired at the bending moment and from shear forces which are transmitted from each beam bolt group. Calculation results according to the suggested method show good agreement of laboratory experimental results of specimens with numerical simulations. Two specimens of beam-to-column connections were tested in the laboratory. Lateral supports were used on the specimens to prevent lateral displacements in order to better investigate the behaviour of the rectangular gusset plate in plane. Experiments were simulated by modelling rectangular gusset plates using standard finite element software ANSYS Workbench 14.0. Three-dimensional solid elements were used for modelling and both geometric and material nonlinear analysis was performed.

Design of haunches in structural steel joints

The paper presents research in design of haunches in structural steel joints. Experimental results of six speci­mens of haunches with and without flanges are presented. Three specimens are without flanges and three specimens are supported by additional flanges. Flanges differ in stiffness to observe the increase in haunch resistances and the effect on buckling shapes. The research finite element model (RFEA) is studied by material and geometrical nonlinear finite element analysis with imperfections under the actual stress conditions and validated on the measured experimental data. The validity is demonstrated on the comparison of load-deflection curves, failure modes, stress distributions and yield line patterns. The stability analysis of a joint with a haunch is related to the research into component based finite element models of complex joints. The input and the results of the research finite element model are summarised in a benchmark case of a haunch with a flange. A numerical study illustrates the effect of the flange stiffness on the joint’s resistance. The effect is demonstrated on a simple arrangement with triangular stiffeners and on a beam-to-column joint. The main goal of the research is to verify proposed design procedure for stiffeners in steel joints.

Comparisons of Buckling Capacity Curves of Pressurized Spheres with EDR Provisions and Experimental Results

Existing provisions leading to the assessment of the buckling resistance of pressurised spherical shells were published in the European Design Recommendations (EDR) [1]. This book comprises rules which refer to the stability of steel shells of different shapes. In the first step of the general procedure they require calculation of two reference quantities: the elastic critical buckling reference <i>p</i><sub>Rcr</sub> and the plastic reference resistance <i>p</i><sub>Rpl</sub>. These quantities should be determined in the linear buckling analysis (LBA) and in the materially nonlinear analysis (MNA) respectively. Only in the case of spherical shells the existing procedure has exceptional character. It is based on the geometrically nonlinear analysis (GNA) and on the geometrically and materially nonlinear analysis (GMNA), respectively. From this reason, in this particular case there was a need to change the existing approach. The new procedure was presented in the work of Błażejewski & Marcinowski in 2016 (comp. [2]). All steps of the procedure leading to the assessment of buckling resistance of pressurized steel, spherical shells were presented in this work. The elaborated procedure is consistent with provisions of Eurocode EN1993-1-6 (comp. [3]) and with recommendations inserted in Europeans Design Recommendations [1]. The proposed capacity curves were compared with existing proposal published in [1] for three different fabrication quality classes predicted in [3]. In this work also comparisons of author’s proposals with experimental results obtained by other authors were presented.

Nonlinear bending of box section beams of finite length under uniformly distributed loading

In this paper, the bending response of box-section beams of finite length is investigated by using energy methods. The basic assumptions used in the present study are that the total strain energy of a box-section beam subjected to uniformly distributed loading can be simplified into a two-stage analysis process. One is the local bending response of the webs and flanges behaving as plates; the other is the overall bending response of the beam with a deformed cross-section. Analytical solutions for both static and dynamic instabilities of box section beams of finite length subjected to transverse uniformly distributed loading are derived by applying the minimum potential energy principle. To validate the analytical solutions developed, geometric nonlinear finite element analyses are also conducted. Good agreement between the present solutions and the FEA results is demonstrated. Finally, the effects of beam length on the limit critical uniformly distributed load are also discussed.

Structural stability of cable-stayed bridges during construction

This paper presents an investigation of the stability characteristics of steel cable-stayed bridges during construction. In general, cable-stayed bridges are subjected to quite large compressive forces induced by stayed cables, and may become unstable during their construction stage, due to the excessive compressive forces induced by added construction loads. To solve the structural instability problems of the bridges under construction, a nonlinear analysis program was developed based on the theory of nonlinear finite element analysis. The complex stability characteristics of cable-stayed bridges during construction were investigated through a series of rigorous geometric nonlinear analyses, including various structural nonlinearities such as cable-sag effect, beam-column effect of girder and mast, large displacement effect, and girder-mast-cable interaction. To consider the construction characteristics of the cable-stayed bridges, a three-step analysis method is proposed, and used in the present study. In addition, the effects of various cable-arrangement types and girder-mast stiffness ratios on the stability characteristics were extensively investigated. Typical buckling modes can be classified into two categories, depending on the location of critical member or members.

Parametric Study for Bearing Strength in Cold-Formed Steel Bolt Connections

The parametric study method was applied to study the strength of cold-formed steel bolt connection under in-plane loading. Finite element analysis with shell elements was used to model the cold-formed steel plate while solid elements were used to model the bolt fastener for the purpose of studying the structural behavior of bolt connections. Material nonlinearities, contact problems and geometric nonlinearity analysis were carried out to predict the ultimate strength and failure mode of the bolt connections. The finite element results showed that the proposed model accurately represents the failure mode and ultimate strength of a bolt connection, as determined from the experimental investigation. The bearing failure mode was detected in the finite element analysis and the experimental test. Utilizing the results of the parametric study, the outcome of the bolt diameter and the plate thickness on the bearing resistance of cold-formed steel connection was investigated and a new bearing factor parameter is proposed to improve the design standard equation.

Parametric test for the preliminary design of suspension bridges

The preliminary design of suspension bridges is a very important step in the design of a structure, since this stage is the one that will lead to an efficient and economic structure. The models that are used nowadays are complex and sometimes hard to apply, leading to a lack of comprehension from the designing team. This work proposes a new simplified method for the preliminary design of cable suspension bridges that relate the stiffness of the deck truss with the stiffness of the cable, in which stresses are calculated. This relation is intended to know how much of the live load is absorbed by each of these elements and finally obtaining the pre-design values of each substructure. First simple parametric tests are executed using the proposed method and finite element method with geometrical non-linear analysis, in order to study its accuracy. Finally, a real case study is analysed using a known Portuguese suspension bridge, in which the proposed method is applied and compared with numerical solutions.

Nonlinear geometric analysis on Finsler manifolds

This is a survey article on recent progress of comparison geometry and geometric analysis on Finsler manifolds of weighted Ricci curvature bounded below. Our purpose is twofold: give a concise and geometric review on the birth of weighted Ricci curvature and its applications; explain recent results from a nonlinear analogue of the \({\Gamma }\)-calculus based on the Bochner inequality. In the latter we discuss some gradient estimates, functional inequalities, and isoperimetric inequalities.

A multistable tensegrity structure with a gripper application

Multistable tensegrity structures are a new interesting class of compliant prestressed structures. Due to their beneficial properties, these structures are attractive for robotic applications. In this paper a gripper is introduced, which is based on a mechanical compliant, multistable tensegrity structure. The underlying tensegrity structure of the considered gripper is investigated in detail. The influence of the member parameters on the existence of multiple states of self-equilibrium and the mechanical compliance is discussed with the help of static geometric nonlinear analyses, based on the Finite Element Method. The dynamical behaviour of the structure, during the change between the equilibrium configurations, is considered. Therefor the dynamical equations of motion are derived. Then gripper arms are added to the tensegrity structure to obtain a gripper. Different actuation principles for the gripper are discussed. Additionally, a prototype of the gripper has been built and is presented, as well as, selected experimental results.

Applied element method simulation of experimental failure modes in RC shear walls

With the continuous evolution of the numerical methods and the availability of advanced constitutive models, it became a common practice to use complex physical and geometrical nonlinear numerical analyses to estimate the structural behavior of reinforced concrete elements. Such simulations may yield the complete time history of the structural behavior, from the first moment the load is applied until the total collapse of the structure. However, the evolution of the cracking pattern in geometrical discontinuous zones of reinforced concrete elements and the associated failure modes are relatively complex phenomena and their numerical simulation is considerably challenging. The objective of the present paper is to assess the applicability of the Applied Element Method in simulating the development of distinct failure modes in reinforced concrete walls subjected to monotonic loading obtained in experimental tests. A pushover test was simulated numerically on three distinct RC shear walls, all presenting an opening that guarantee a geometrical discontinuity zone and, consequently, a relatively complex cracking pattern. The presence of different reinforcement solutions in each wall enables the assessment of the reliability of the computational model for distinct failure modes. Comparison with available experimental tests allows concluding on the advantages and the limitations of the Applied Element Method when used to estimate the behavior of reinforced concrete elements subjected to monotonic loading.

Comparative analysis of three-dimensional frames by dynamic relaxation methods

ABSTRACTAnalysis of three-dimensional frames is a complex process. Each node of these structures has six degrees of freedom, which results in a large set of governing equations. Investigators have utilized the computer power to extend the application of numerical approaches. One of these methods is named dynamic relaxation technique. This strategy explicitly solves the simultaneous system of equations. In this scheme, the static structural equilibrium equations are converted into a dynamic one by adding fictitious mass and damping. To perform nonlinear geometric analysis of 3D frames, 12 classical DR methods are exploited. Previously, the abilities of these approaches in analyzing these structures have not been compared. In each technique, time step, mass, and damping matrices are obtained based on other researchers' works. The structural behavior is assessed with and without considering the shear deformations. For both cases, the load–displacement curves are depicted. In this article, 11 different frames are analyzed. Since a few nonlinear solutions of 3D frames are available, these structures can be used as a benchmark in the future studies. Finally, the used algorithms are graded based on their required number of iterations and analysis time. Findings prove that the Qiang, Rezaiee-Pajand and Sarafrzi techniques perform more successfully in comparison to the other schemes.

Geometric nonlinear analysis of prismatic shells using the semi-analytical finite strip method

The present study sheds light on geometric nonlinear static analysis of prismatic shells using the semi-analytical finite strip method. A new computational model, which includes a fully nonlinear compound strip with a longitudinal and transverse stiffener, has been presented. Furthermore, strips with non-uniform characteristics in the longitudinal direction have been used in nonlinear analysis. This has, to the best knowledge of authors, never been reported. Also, this paper describes the design and implementation of eighteen ideal boundary conditions using three different longitudinal and six well-known transverse displacement interpolation functions.The results of the presented study were obtained using an open-source software and multi-purpose software Abaqus. Moreover, the accuracy of the applied computational approach has been verified by comparison with results from the literature. An excellent agreement of displacement fields is achieved for large deflection analyses of plates with a hole and stiffeners as well as for shells with a stepped thickness in the longitudinal direction. Additionally, results from post-buckling analyses of thin-walled structures, a snap-through and snap-back behavior of shallow shells, are matched. The work presented here has profound implications for future studies of the finite strip deployment.

Finite Element Model for Nonlinear Analysis of Reinforced Concrete Beams and Plane Frames

Abstract In this work, a two-dimensional finite element (FE) model for physical and geometric nonlinear analysis of reinforced concrete beams and plane frames, developed by the authors, is presented. The FE model is based on the Euler-Bernoulli Beam Theory, in which shear deformations are neglected. The bar elements have three nodes with a total of seven degrees of freedom. Three Gauss-points are utilized for the element integration, with the element section discretized into layers at each Gauss point (Fiber Model). It is assumed that concrete and reinforcing bars are perfectly bonded, and each section layer is assumed to be under a uniaxial stress-state. Nonlinear constitutive laws are utilized for both concrete and reinforcing steel layers, and a refined tension-stiffening model, developed by the authors, is included. The Total Lagrangean Formulation is adopted for geometric nonlinear consideration and several methods can be utilized to achieve equilibrium convergence of the nonlinear equations. The developed model is implemented into a computer program named ANEST/CA, which is validated by comparison with some tests on RC beams and plane frames, showing an excellent correlation between numerical and experimental results.

Quadratic prismatic and hexahedral solid–shell elements for geometric nonlinear analysis of laminated composite structures

The current contribution proposes two quadratic, prismatic and hexahedral, solid–shell elements for the geometric nonlinear analysis of laminated composite structures. The formulation of the proposed solid–shell elements is based on a fully three-dimensional approach combining the assumed-strain method and the reduced-integration technique. In particular, only translational degrees of freedom are considered in the formulation and a preferential direction is chosen as the thickness direction, along which an arbitrary number of integration points are arranged. Making use of different physical local frames, these elements are coupled with fully three-dimensional orthotropic constitutive equations, which allows modeling multilayered composite structures with only a single element layer through the thickness. A series of popular nonlinear benchmark tests for laminated composite structures is performed to assess the performance of the proposed SHB elements. Compared to reference solutions taken from the literature, the results provided by the SHB elements show excellent agreement. Moreover, on the whole, the proposed SHB elements perform better than state-of-the-art ABAQUS elements, which have the same geometry and kinematics, using comparable mesh discretizations.