Nonlinear Structural Analysis Research Articles

Analisis Tidak Langsung Pada Desain Terhadap Stabilitas Struktur Gedung Baja

There are three methods of design for stability defined in AISC 360-16 Specification for Structural Steel Buildings, namely Direct Analysis Method (DAM), Effective-Length Method (ELM), and First-Order Analysis Method (FOM). DAM is the method that is featured by AISC. Based on DAM, Rafael Sabelli proposed another method called Indirect Analysis Method (IAM). IAM is a new method that has not generally been used, and also has not been included in the AISC Specification. This research is conducted in order to study IAM and compares the analysis results of IAM with those of DAM. Using a nonlinear structural analysis software, design and analysis were conducted for stability design of an eight-story building loaded with dead load, live load, and wind load. IAM provides a simple amplifier approach which is called B3 to address the member inelasticity, member imperfections, and uncertainty in member stiffness. From the study that has been conducted, the analysis results using IAM show close values with those of DAM, in terms of demand-to-capacity ratios, with IAM is more conservative than DAM. The use of IAM simplifies the design process without affecting the economy of the design.

Damping approaches in nonlinear seismic time history analysis for large mobile equipment with uplift

AbstractIn large mobile equipment in seismically active regions, seismic stability is often a decisive design criterion, and the behaviour of this large equipment, which is characterised by uplift, tilting and rocking, can only be calculated by means of nonlinear time history analyses. Here, the model damping approach has a significant influence on the results of these analyses but there are no scientific approaches for large mobile equipment with nonlinear behaviour such as uplift. In this paper, possible theoretical damping approaches for nonlinear time history analysis of structures with uplift such as large mobile equipment are discussed and numerical studies are conducted to investigate the influence of damping in the model on the concise results of the typical behaviour of large mobile equipment under seismic excitation. A suitable new approach is to be developed and a way of practical implementation is being prepared. Experimental studies on real typical bucket wheel machines will identify and validate important natural frequencies and associated damping for the numerical approach. These can be applied in numerical models using the damping approach engineered in the theoretical part. Thus, realistic results of the numerical models under nonlinear seismic time history analyses can be expected and more precise conclusions on the distinctive behaviour of large mobile equipment with uplift can be drawn.

Parametric modeling logic analysis and precision control method application of nonlinear landscape structures based on Rhino+Grasshopper platform: A case study of the Flying Goose viewing platform in Beijing

The development of digital technology has made non-linear landscape structures mainstream and has brought new challenges to design methods. The efficiency and accuracy of applying Rhino+Grasshopper parametric modelling to such structures has gained the attention of design practitioners and scholars. However, there are still research gaps in this approach in current research. Therefore, this study uses the Flying Goose viewing platform as a case study to supplement the lack of specific case studies on non-linear landscape structures; it analyses the modelling logic through three parts: morphological characteristics, structural system, appendages and decoration to supplement the lack of systematic knowledge on modelling logic; it analyses the four methods of unfolding control, isometric projection, function shaping and linear interference. The analysis and discussion of the four core precision control methods used in the Rhino+Grasshopper parametric modelling process complements the current lack of specific research on Rhino+Grasshopper parametric modelling morphological precision control methods. The aim is to provide a systematic analysis of the modelling logic of non-linear landscape structures and a detailed analysis of the precision control methods on top of the non-linear landscape structures morphological realisation, providing a theoretical basis and application examples for future research of the same type.

Improving composite cable performance: Nonlinear thermo-elastic analysis with temperature-dependent pretension and 3D cable elements

Composite cables are widely used in various engineering applications due to their high strength-to-weight ratio and versatility. However, their performance is highly influenced by temperature changes and the application of pretension, which must be considered to perform accurate analysis. Fibrous materials, characterized by their high strength and flexibility, are incorporated into the cable structure to enhance its performance. This research paper presents a comprehensive study on the nonlinear analysis of cable structures made of fibrous materials considering temperature-dependent effects and pretension. A three-dimensional cable element model is employed to accurately capture the complex behavior of composite cables. The proposed approach allows for a more realistic representation of the cable's response, accounting for both mechanical and thermal effects. In order to effectively solve nonlinear equations, the Newton-Raphson (NR) method, a powerful iterative technique for solving nonlinear equations, is employed. This technique is employed to analyze the behavior of composite cables under various loading conditions, accounting for factors such as temperature dependence and pretension. Through extensive numerical simulations, the effects of temperature variation and pretension on the structural performance of composite cables are evaluated. The results provide valuable insights into the behavior of composite cables and offer guidelines for optimizing their performance in real-world applications. This research contributes to advancing composite cable design and engineering practices by considering the intricate interplay between temperature-dependent behavior, pretension, and nonlinear thermo-elastic analysis.

Optimal design of friction tuned mass damper for seismic control of an integral bridge

Vibration control systems such as tuned mass damper (TMD) have drawn considerable attention due to their ability to reduce the seismic response of structures and the consequent damage. The present paper investigates the performance of a new type of TMD, called the friction tuned mass damper (FTMD), in decreasing the seismic response of a four-span integral bridge. The performance of the FTMD in then compared with the TMD under various conditions. The parameters of both dampers are computed via an optimization method. The bridge with damper is then subjected to several strong earthquakes in the transverse direction in different intensity levels, ranging from 0.2 g to 0.8 g. The Particle swarm optimization with passive congregation (PSOPC) is employed and carried out in MATLAB, while the structural modeling and nonlinear dynamic analysis of the bridge is programmed in OpenSees. Numerical results indicate that the FTMD performs better than the TMD in reducing the displacement of the deck. At low intensity of 0.2 g, the reduction in the displacement response of the deck by the TMD and the FTMD are about 28% and 40%, respectively. These values reach 8% and 15% at intensity of 0.8 g. Therefore higher earthquake intensity significantly undermines the performance of both dampers. However the superior performance of the FTMD compared to the TMD is observed.

Comparison of ACI-318 and TS-500 codes for nonlinear seismic analysis of RC structures using force-based fiber element approach

The material properties such as compressive strength, tensile strength, and modulus of elasticity have been significant phenomena in the nonlinear seismic analysis of RC structures. In several national codes, different equations for the material properties of concrete based on compressive strength are suggested. The effectiveness of these equations in the analysis of RC structures should be investigated to determine the seismic response of the structure. In this study, the effectiveness of ACI-318 and TS 500 design codes is investigated in the numerical modeling of RC structures. For this purpose, the seismic responses of two RC structures experimented in the laboratory are used. The first structure is a two-dimensional three-bay and four-story RC bare frame structure that was tested in European Laboratory for Structural Assessment. The second structure is an RC tall bridge pier that was tested at Pacific Earthquake Engineering Research Center. The numerical solutions are obtained by using the Force-based Fiber Element Approach. The experimental and numerical analysis results are compared in terms of top displacements and damage zones. The concrete material properties which provide the best approximation to the experimental results are investigated for both design codes. It is concluded that the material properties of RC structures determined according to the ACI-318 code can be used for the Force-based Fiber Element Approach with regard to displacement response and damage regions.

A novel Woodbury solution method for nonlinear seismic response analysis of large‐scale structures

AbstractThe Woodbury formula is an efficient tool in mathematics to calculate low‐rank perturbation problems and has been applied to improve the computational efficiency of nonlinear seismic response analysis (NSRA) of structures with local nonlinearity. Using the Woodbury formula for NSRA can avoid the time‐consuming recalculation and factorization of the large‐dimensional global stiffness matrix of a structure by only solving a small‐dimensional Schur complement system representing local nonlinearity per iteration. Because the dimension of the Schur complement matrix is determined by the inelastic degree of freedom (IDOF) number, which represents the scale of local nonlinear regions, a small IDOF number is helpful for achieving the high‐efficiency advantage of the Woodbury formula. However, when performing NSRA for large‐scale structures, the IDOF number is usually relatively large, which contradicts the efficiency requirement of the Woodbury formula. To solve this problem and extend the advantage of the Woodbury formula to the NSRA of large‐scale structures, this paper first proposes a two‐stage IDOF number reduction method by eliminating the IDOFs that have insignificant effects on the results, and consequently, a variant Woodbury formula is derived. Because only the principal component in the Schur complement matrix is retained, the dimension of this matrix and the cost for factorizing it can be reduced significantly without losing accuracy, thus greatly improving the efficiency of the proposed method. Moreover, to reduce the additional computational time introduced by the IDOF number reduction procedure and to further improve the computational performance of the proposed method, an OpenMP parallel computational strategy is incorporated. Finally, the validity of the proposed method is verified by implementing incremental dynamic analysis for a large‐scale reinforced concrete structure.

Reliability of Response-Controlled Stepped Sine Testing for Experimental Detection of Nonlinear Structure

Nonlinear structural dynamic analysis is required for mechanical structures experiencing nonlinearity through large force-vibration response ranges. Nonlinearities can be caused by large vibration displacements, material properties, or joints. Experimental modal analysis for nonlinear detection is achieved using conventional force-controlled stepped sine testing. However, this approach often encounters premature jumps in frequency response curves before reaching actual resonance peaks. In recent years, response-controlled stepped sine testing (RCT) has been introduced to precisely quantify resonant peaks. This approach, however, has only been limitedly utilised to detect and analyse nonlinearity in jointed structures and structures experiencing large displacement. In this paper, the reliability of the RCT approach is assessed for detecting nonlinearity from different sources. The experimental setup involves placing two magnets on opposite sides of a plate's free end to induce localised nonlinearity through magnet attraction. A low force magnitude of random excitation is employed to identify the frequency range of the first vibration mode using an electromagnetic shaker. Subsequently, RCT is performed within this range to measure the nonlinear forced response. Frequency response functions are measured at ten different controlled displacement amplitudes at the driving point. The analysis observed a symmetry curve of response in the measured FRFs. The results indicate that nonlinear hardening is detected at structures with localised magnet attraction. In conclusion, the reliability of applying the RCT approach for detecting nonlinearity from magnet attraction is achieved due to the absence of a jump issue in FRFs.

A smart component model replacement approach for refined simulation of large nonlinear RC structures

This paper proposes a novel smart component model replacement (SCMR) approach that is not only efficient for large-scale nonlinear structural analysis, but also accurate in the refined simulation of components of interest. The method creates a FE model with a relatively coarse mesh to simulate the entire structure. During analysis, when a component is identified to predefined criteria defined by the users, its model will be replaced by another more refined “substructure” model that can simulate the damage and failure more accurately. A few “replacement” strategies are presented for smoothly transiting between different models: (1) A gradually transiting strategy is presented to avoid the possible jumps of responses due to the model differences to guarantee numerical stability; (2) The historical boundary conditions are applied to the substructure model to address the historical dependence of responses; (3) The boundary connection between main and substructure is considered by using a flexible client/server technology, to simplify the replacement. The SCMR approach is verified by three application examples. The results demonstrate that the proposed modeling approach can efficiently perform large-scale nonlinear structural analysis, while capturing the failure mechanism in RC structures well.

Development of practical downsampling methods for nonlinear time history analysis of complex structures

One of the main problems of nonlinear time history analysis is its high computational effort, especially in structures with large number of structural components, high-rise buildings and complex structural systems. The ground motions recorded in recent years also include more recorded points than in the past, which has also increased the required volume of calculations. In this paper, three downsampling methods for reducing calculation costs of nonlinear time history analysis are presented and their applicability is investigated through practical examples of complex structures. These methods include the discrete wavelet transform, the time step correction, and the wavelet time step correction which is introduced in this paper. The efficiency of these downsampling methods is investigated for near-fault and far-fault earthquake records, as well as for records on different soil types. A comprehensive study is performed on five sets of ground motions consisting of 20 records. Each record is filtered up to three stages using one half, one quarter, and one eighth of the number of the main record points. First the linear and nonlinear response spectra based on the original records and the approximate waves are investigated. Subsequently, to evaluate the performance of the methods on more complex structural systems, two three-dimensional structures of 6-story and 15-story are analyzed. The 6-story structure is equipped with viscous dampers, while the 15-story structure has seismic isolators. The results indicate that the wavelet time step correction method has better performance in most cases, compared to the other two methods. It is shown that careful consideration is needed when dealing with earthquake records with high frequency contents. In such situations, one filtering step for the discrete wavelet transform method and two filtering steps for the other two methods are recommended. Also, in practical applications, it is advisable to choose earthquake records exhibiting the least error based on the results of SDOF systems analyses. Employing this technique can significantly cut down computational effort (up to 90%), while maintaining an average error ranging from 1% to 2% for the wavelet time step correction method.

Applying Potra-Pták Iterative Cycle for Solving Highly Nonlinear Structural Problems

When solving nonlinear algebraic equations that arise from discretization using the finite element method (FEM), it is often observed that the standard Newton-Raphson (N-R) iteration either fails to converge or necessitates a large number of iterations in the vicinity of critical points. This work proposes an additional numerical strategy, known as the Potra-Pták iterative cycle, to improve the efficiency of solving highly nonlinear structural problems. Therefore, the focus here is on making the nonlinear solver more robust and efficient, allowing the analysis of more complex nonlinear structures. In the Potra-Pták iterative cycle, two corrections of the objective function (energy function) are performed. The introduction of a second correction in the iterative cycle makes the Potra-Pták strategy more efficient than the standard or modified N-R iterations. This numerical strategy was implemented in the homemade Computational System for Advanced Structural Analysis (CS-ASA) program. The program is based on the FEM and is capable of performing static and dynamic nonlinear analysis of steel, concrete, and composite structures, and its efficiency is then verified through the analysis of slender frames and arches. The algorithm details for solving the nonlinear structural problem, characterized by the Potra-Pták scheme, are provided.

Geometrically nonlinear analysis of steel structures with nonsymmetric sections under elevated temperatures

Steel members using nonsymmetric sections are envisioned as popular because of the advancement in manufacturing techniques, in which frame analysis method under extreme scenarios, such as fire hazards, has not been thoroughly established. The element formulation for those members has been commonly derived based on either the updated-Lagrangian (UL) or the total-Lagrangian (TL) methods. However, the UL method is difficult to analyze the steel member exposed to fires because the previous equilibrium conditions may be destroyed due to the material stiffness degradation at elevated temperatures. Nevertheless, the TL method can be used for studying steel members under fire, but it is inefficient, time-consuming, and requires starting-over computation at every temperature increment. To this, the co-rotational (CR) method could be a promising solution for tackling the analysis problems of steel members in fire efficiently and accurately. The CR method separately describes the element and its rigid body movements, such that the material stiffness degradation can be considered at the element level without the starting-over computation at new temperature increments, which is numerically efficient. This paper reformulates the beam-column element formulation with the warping degree of freedom for nonsymmetric section members using the CR method, which can conveniently consider the material degradation and the thermal expansion for the analysis of steel members at elevated temperatures. The lateral-torsional and flexural-torsional buckling of nonsymmetric section members can be captured robustly. Detailed derivation for element formulation is given, and several examples are provided for verifying the accuracy and examining the robustness of the proposed method.

A co-rotational formulation for quasi-steady aerodynamic nonlinear analysis of frame structures

The design of structures submitted to aerodynamic loads usually requires the development of specific computational models considering fluid-structure interactions. Models using structural frame elements are developed in several relevant applications such as, the design of advanced aircraft wings, wind turbine blades or power transmission lines. In the case of flexible frame structures submitted to fluid flows, the computation of inertial and aerodynamic forces for large displacements and rotations is a challenging task. In this article, we present a novel formulation for the efficient computation of aerodynamic forces in frame structures, coupling the co-rotational framework with the quasi-steady theory. A numerical procedure is provided considering a tangent matrix for the aerodynamic forces. This formulation is implemented in the open-source library ONSAS, allowing users to reproduce the results or solve other frame nonlinear dynamic problems. The proposed formulation and its implementation are validated through the resolution of four numerical examples. The formulation and the numerical procedure proposed efficiently provide accurate solutions for these challenging problems with large displacements and rotations.

Efficient numerical implementation for nonlinear analysis of pile-supported structures during soil liquefaction through adaptive pile element formulations

The structural behavior of pile-supported structures during soil liquefaction is sometimes insufficiently investigated properly due to the inefficiency in the existing line finite element method (LFEM), which is widely used in practice. The traditional LFEM to simulate pile response requires dense element mesh for accurate results, as it simplifies the continuous surrounding soil as discrete spring elements, resulting in high computational costs, especially for pile-supported structures with a significant number of piles. Additionally, analyzing pile-supported structures in different stages of soil liquefaction requires repetitive updating of p-y curves and tedious starting-over iteration processes. To address these issues, an innovative line element formulation named the pile element formulation is employed and improved to adaptively simulate the surrounding soil conditions at different stages during liquefaction within the element formulation, eliminating the need to model discrete soil springs and significantly improving computational efficiency. The adaptive pile element formulation is then implemented within a refined Newton-Raphson iteration procedure that is proposed for a more effective nonlinear analysis process to consider soil liquefaction without repetitive iteration processes from starting over. Through several examples, the computational efficiency of the proposed method is validated, which requires only 20% of the computational cost compared to traditional LFEM while still providing accurate results, highlighting the application potential of the present study.

Three-dimensional plasticity-based topology optimization with smoothed finite element analysis

AbstractThis paper presents a novel plasticity-based formulation for three-dimensional (3D) topology optimization of continuum structures. The proposed formulation addresses the optimization problem by combining mixed rigid-plastic analysis with density-based topology optimization, resulting in a volume minimization approach. Unlike conventional stress-constrained topology optimization methods that rely on linear elastic structural analysis, our developed formulation focuses on enhancing the loading capacity of the designed structures based on the plastic limit theory, leading to more cost-effective designs. To improve computational efficiency, we employ the smoothed finite element technique in our proposed method, enabling the utilization of linear tetrahedral elements for 3D mesh refinement. Moreover, the final formulation of our developed method can be efficiently solved using the advanced primal–dual interior point method, eliminating the need for a separate nonlinear finite element structural analysis. Numerical examples are presented to demonstrate the effectiveness of the proposed approach in offering enhanced design possibilities for continuum structures.

Review of Wind-Induced Effects Estimation through Nonlinear Analysis of Tall Buildings, High-Rise Structures, Flexible Bridges and Transmission Lines

The nonlinear effects exhibited by structures under the action of wind loads have gradually stepped into the vision of wind-resistant researchers. By summarizing the prominent wind-induced nonlinear problems of four types of wind-sensitive structures, namely tall buildings, high-rise structures, flexible bridges, and transmission lines, the occurrence mechanism of their nonlinear effects is revealed, providing cutting-edge research progress in theoretical studies, experimental methods and vibration control. Aerodynamic admittance provides insights into the aerodynamic nonlinearity (AN) between the wind pressure spectrum and wind speed spectrum of tall building surfaces. The equivalent nonlinear equation method is used to solve nonlinear vibration equations with generalized van-der-Pol-type aerodynamic damping terms. The elastic–plastic finite element method and multiscale modeling method are widely employed to analyze the effects of geometric nonlinearity (GN) and material nonlinearity (MN) at local nodes on the wind-induced response of latticed tall structures. The AN in blunt sections of bridges arises from the amplitude dependence of the aerodynamic derivative and the higher-order term of the self-excited force. Volterra series aerodynamic models are more suitable for the nonlinear aerodynamic modeling of bridges than the polynomial models studied more in the past. The improved Lindstedt–Poincare perturbation method, which considers the strong GN in the response of ice-covered transmission lines, offers high accuracy. The complex numerical calculations and nonlinear analyses involved in wind-induced nonlinear effects continue to consume significant computational resources and time, especially for complex wind field conditions and flexible and variable structural forms. It is necessary to further develop analytical, modeling and identification tools to facilitate the modeling of nonlinear features in the future.

Morpho-logic from a topos perspective – application to symbolic AI

Modal logics have proved useful for many reasoning tasks in symbolic artificial intelligence (AI), such as belief revision, spatial reasoning, among others. On the other hand, mathematical morphology (MM) is a theory for non-linear analysis of structures, that was widely developed and applied in image analysis. Its mathematical bases rely on algebra, complete lattices, topology. Strong links have been established between MM and mathematical logics, mostly modal logics. In this paper, we propose to further develop and generalize this link between mathematical morphology and modal logic from a topos perspective, i.e. categorial structures generalizing space, and connecting logics, sets and topology. Furthermore, we rely on the internal language and logic of a topos. We define structuring elements, dilations and erosions as morphisms. Then we introduce the notion of structuring neighborhoods, and show that the dilations and erosions based on them lead to a constructive modal logic, for which a sound and complete proof system is proposed. We then show that the modal logic thus defined (called morpho-logic here), is well adapted to define concrete and efficient operators for revision, merging, and abduction of new knowledge, or even spatial reasoning.

A mixed micromechanical homogenisation scheme for the prediction of the 3D orthotropic elastic properties of different masonry bond typologies

Masonry structures composed of two distinct material phases (units and mortar) with potentially vastly different elastic properties are characterised by strong orthotropy. The variety of commonly employed bond typologies for masonry walls, featuring unit groups and mortar joints with different orientation with respect to the plane of the wall, result in complex stress and strain interactions between the material phases. This interaction is further complicated by the high volume ratio of the units within the masonry composite. Therefore, classical homogenisation schemes for matrix-inclusion composite materials, mortar being the matrix and units the inclusions, are suitable for only a narrow range of relative unit and mortar stiffness, expressed as the ratio of the Young’s moduli of the two phases. This feature makes their application in nonlinear analysis of masonry structures, which have a strong tendency to crack under mechanical loading, problematic.The paper presents a novel homogenisation scheme based on different mean-field homogenisation schemes combined through a process derived from the discretisation of the masonry cells using a method-of-cells approach. This approach allows the intuitive interpretation of the stress and strain interaction of the material phases and yields good predictions of the elastic properties of a variety of masonry bonds over an extensive range of relative unit and mortar stiffness.

Non-Linear Structural Analysis of Shear Flexible FGM Beams

Non-linear structural response of Functionally Graded Material (FGM) beams is studied using the finite element method. The deformations obtained using Euler-Bernoulli beam and Timoshenko beam theories are compared for different length to height ratios, volume fraction exponents and boundary conditions. The percentage errors in lateral deformations for neglecting the effects of shear flexibility are discussed in detail. Through thickness variation of the axial stress shows a shift in the neutral axis from the mid-thickness of beam for homogenous as well as FGM beams and for the boundary conditions considered. The range of volume fraction exponents for the practical design of FGM beams is suggested to avoid steep stress gradients.

A Novel Geometric Nonlinear Analysis Method for Planar Beam Structures Based on Co- Rotation and Substructure Method

Nonlinear behavior analysis of structures using finite element methods requires multiple iterative solutions. Therefore, improving computational efficiency while ensuring the accuracy of nonlinear calculations is crucial. In this paper, a new geometric nonlinear analysis method for planar beam structures is proposed, based on the co-spinning method and the substructure method, using a substructure containing two planar beam elements as an example. The co-spinning method accurately calculates small deformations by subtracting rigid body displacement from the large displacement of the structure. The substructure method condenses the degrees of freedom of internal nodes into boundary nodes, greatly reducing the order of the nonlinear equilibrium equation group of the structure. The two methods are combined, and a calculation program is developed using the arc length method, which has good performance in solving nonlinear equation groups. Two classic examples are used to verify the correctness of the proposed method by comparing the results with existing literature.