Nonlinear Structural Analysis Research Articles

Computational evaluation of flight performance of flapping-wing nano air vehicles using hierarchical coupling of nonlinear dynamic and fluid-structure interaction analyses

This study endeavours to introduce an inventive hierarchical coupling methodology for evaluating the flight capabilities of polymer micromachined flapping-wing nano air vehicles (FWNAVs) using advanced computational tools. Furthermore, our objective is to provide a practical demonstration of FWNAVs in both tethered and airborne scenarios. These dual objectives represent the distinctive and pioneering aspects of this research. Such FWNAVs, which are insect-inspired robots, have a 2.5-dimensional structure. An FWNAV comprises a micro piezoelectric drive system and a pair of micro thin flexible wings. The drive system includes a micro transmission and a piezoelectric bimorph actuator. The flight performance of the designed FWNAV is evaluated using a hierarchical coupling approach, where the whole system is decomposed into a micro wing and a micro piezoelectric drive system. The coupling between these parts is modelled as one-way coupling and that between the micro wings and the surrounding air is modelled as strong coupling. In the one-way coupling analysis, nonlinear structural dynamic analysis is conducted for the micro piezoelectric drive system, where the dynamic response is transmitted to the micro wings via the Dirichlet boundary condition. In the strong coupling analysis, strongly coupled fluid-structure interaction analysis is conducted for the micro wings and the surrounding air to consider their strong coupling. The optimisation of flight performance is conducted using fluid-structure interaction analysis to achieve sufficient lift force to support the weight of an FWNAV. The design of a tethered and flyable FWNAV with a size of 10 mm or smaller is demonstrated. This FWNAV can be easily fabricated using polymer micromachining.

Nonlinear equivalent sdof analysis of steel frame structures using parameters estimated from recorded floor acceleration response: An experimental case study

In practice, the building displacement response is often estimated from acceleration using double integration due to the expensiveness and difficulty of measuring displacement. However, a high-pass filter is needed to eliminate the low-frequency component due to the existence of indistinguishable lowfrequency noise that incurred during the double integrating process. As a result, the displacements obtained from accelerations may have large errors, especially when the structure has significant nonlinear deformation. This study aims to estimate the displacement response of steel frame structures by firstly estimating SDOF hysteretic parameters from the acceleration response data, and then by performing numerical analysis using the extracted hysteresis model. The proposed approach was verified using experimental data from shaking table test of three identical 5-story steel frame structures subjected to different seismic records. The results show that the SDOF analysis maximum displacement has higher accuracy than the equivalent SDOF maximum displacement estimated from recorded floor acceleration response data that is recently used for post-earthquake building assessment.

A Review on Seismic Analysis of RCC and Steel Structures using Linear and Non-linear Static Analysis

Abstract: An earthquake can cause significant harm to various aspects, including buildings, general life, and particularly multistory structures. In India, structures constructed in earthquake-prone regions, as defined by IS 1893: 2002, must be designed to withstand the loads, stresses, and consequences of earthquakes. Several techniques are available for assessing multi-story structures in this context, such as the Response Spectrum Method, Equivalent Lateral Force Method, Time History Method, and adhering to specific code provisions. Numerous researchers have undertaken studies to analyze multi-story buildings using one or more of these methods. However, there exists still a confusion about an effective and efficient method preferred for seismic design of multi-story buildings. Among the various approaches, the seismic coefficient method and response spectrum method are the most widely used. This comparative investigation aims to review research reports that have employed the Equivalent Lateral Force Method and Response Spectrum Method to analyze multi-story buildings in earthquake-prone areas. The design response spectrum serves as the initial reference point for most established seismic design and assessment procedures. It primarily dictates the inertia forces that buildings and structures must withstand during an earthquake. This paper aims to introduce and discuss contemporary concepts regarding the creation and utilization of earthquake design response spectra. Additionally, the paper highlights the various methods of seismic analysis being investigated in the past literature. It also gives an overview of various investigations being carried out using linear and non-linear static analysis of RCC structures. Many of the ideas presented are specifically aimed at aiding engineers who work in regions with low to moderate seismic activity. The main objective is to inform engineers about modern approaches to developing response spectra. This knowledge can then be applied effectively in both analytical and design contexts when dealing with earthquake-related challenges

An ameliorative duration of pulse-like ground motion records for nonlinear structural analysis

The near-field pulse-like ground motion contains obvious long-period and large pulse characteristic, which makes the nonlinear response of the structure exceed the general prediction of seismic response results. In order to reserve the obvious pulse component while selecting the strong ground motion duration part of the near-field pulse-like ground motion record without causing a large loss of spectral characteristics, the paper proposes an ameliorative truncated strong ground motion duration—useful duration. It is proposed based on the elastic acceleration response spectrum. Its principle is to make the acceleration response spectrum corresponding to useful duration and that corresponding to the original ground motion record as close and consistent as possible. The research results show that from the perspective of elastic response spectrum matching, the response spectrum matching error corresponding to useful duration is smaller than that of significant duration. In addition, the five types of periods corresponding to useful duration are closer to the period of original ground motion. Ulteriorly, from the displacement ratio spectrum of the elasto-plastic single-degree-of-freedom system, it is found that the average value of the elasto-plastic displacement ratio spectrum of useful duration and the original ground motion record is 0.98, which is very close to 1.00. It shows that the truncated ground motion can be used to replace the original ground motion to fully predict the nonlinear response of typical structures. Additionally, the effectiveness is further verified in the nonlinear response of three reinforced concrete frame structures, and the nonlinear response results of the structures are calculated using the time-history of useful duration, with less discreteness.

A corotational isogeometric assumed natural strain shell element in updated lagrangian formulation for general geometric nonlinear analysis of thin-walled structures

A new general geometric nonlinear curved quadrilateral shell element, which can handle large displacements and large rotations, is presented in this paper. It is formulated based on the incremental virtual work equation in updated Lagrangian formulation for general large displacement analysis. The kinematics of shell element is described using non-uniform B-spline patch, which results in the element displacement field with higher order continuity and the element performance more resistive to shear locking and membrane locking. In order to perfectly avoid such membrane locking and shear locking behaviors, the assumed in-plane membrane strain field and the assumed transverse shear strain field for the incremental covariant Green-Lagrange strain are constructed as linear combinations of non-uniform B-spline basis functions with degrees lower than those adopted by the original displacement field interpolation. In addition, based on Euler parameters, the corotational procedure available for high order isogeometric shell element is developed to extract the strain-producing deformational displacements and rotations and to update the element stresses and realistic internal force vectors. The accuracy and robustness of proposed shell element are demonstrated through the solutions of various benchmark problems.

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.