Nonlinear Structural Analysis Research Articles

Seismic hazard study for the duration of ground-motions triggered by intraslab earthquakes

AbstractThis paper presents a probabilistic seismic hazard analysis for the duration of ground motions in Mexico City caused by intraslab earthquakes. The study implies establishing criteria to measure the duration of ground motions and developing predictive equations (GMPEs) for its estimation. Focus is placed on the relative significant duration, $$D_{Sr}$$ D Sr , which is based on the accumulation of energy of ground motions. The study extends to the development of hazard curves that allow estimating the annual probability of exceedance of said parameter. The scope is limited to ground motions caused by intraslab earthquakes occurring in Mexico and that engineeringly affect its capital, Mexico City, which is in a geographical region where the effects of soil-dynamic amplification are manifested considerably. A strong-motion database that includes 1517 horizontal accelerograms, with peak ground acceleration, $$PGA$$ PGA , greater than or equal to 3 cm/s2, recorded during 21 earthquakes from 1994 to 2023 were used to develop the GMPEs. The quantitative description of the time, size, and spatial distribution of the seismic-activity occurrence was defined using a catalog of 46 earthquakes that occurred from 1900 to 2023. The earthquakes have moment magnitude, $$M_{w}$$ M w , greater than or equal to 6. With the tools developed, amplitude- and duration-based hazard-consistent accelerograms can be simulated and used in nonlinear dynamic analyses (NDAs) of structures. This study includes an application example where three sites in Mexico City are selected to compute inelastic response spectra. Hysteretic-energy demands up to 5 times higher are found after a comparison between the inelastic-response spectra from hazard-consistent accelerograms and those provided by current Mexican regulations.

Nonlinear dynamical modeling and response analysis of complex structures based on assumed mode weighting

The assumed mode method (AMM) is widely used for dynamical modeling but faces increasing challenges in developing low-dimensional and high-precision models of complex structures for investigations of nonlinear dynamical responses and active vibration control. This is mainly because the current complex structure has an increasing number of components, each of which needs to be discretized by multiple assumed modes in dynamical modeling, leading to increasing degrees of freedom for the system. To address this issue, this paper proposes a dimension-reduced method based on the assumed mode weighting method, referred to as Mode Weighting Method (MWM). The modeling process of a multi-beam structure is fully presented as an example to show the strategy of the MWM. During this process, the assumed mode (AM) model (the dynamic model derived in terms of a set of assumed modes) is developed first where the joints of the structure between its components are considered as artificial springs and each component is discretized by its vibration modes without constraints. The components of the eigenvector of the characteristic equation derived from the AM model are taken as the weighting coefficients to get the approximate analytical global modes of the structure by multiplying the corresponding assumed modes. Consequently, a nonlinear dynamic model with a few degree of freedom is obtained by discretizing the structure with the weighted modes. Moreover, a technique for simply obtaining the weighted mode (WM) models by directly processing the AM model through a transformation matrix is presented. To validate the proposed method, the simulations on the natural characteristics and the dynamical responses for both linear and nonlinear models, are performed respectively based on the WM and the finite element models, where both results are well matched each other. This work provides a new way of developing advanced dynamical modeling methods for structural dynamics design, optimization, and active vibration control.

Proposing unsupervised clustering-based earthquake records selection framework for computationally efficient nonlinear response history analysis of structures equipped with multi-stage friction pendulum bearings

The design and analysis of base-isolated structures are critical for ensuring seismic performance and safety. Nevertheless, to effectively design and analyze base-isolated structures, it is essential to consider the structure's response under various ground motions that may occur during an earthquake. The nonlinear response history analysis (NRHA) is a common method for evaluating structures' seismic response under a specific set of ground motions. However, conducting this analysis for many earthquakes can be computationally expensive and time-consuming. Therefore, it is desirable to have a method for selecting a subset of earthquake records representative of the earthquake population. Accordingly, this study introduces a novel block-based framework based on the K-means unsupervised clustering techniques for efficient earthquake records' selection NRHA of base-isolated structures. The proposed approach aims to reduce the number of records required for investigations by identifying clusters of similar seismic signals and selecting representative records from each cluster for the NRHA. Additionally, the proposed framework serves a vital role in identifying the earthquake records that can be used as a training dataset for developing artificial neural network (ANN) models, enabling rapid response estimation of base-isolated structures. This dual functionality of the proposed method provides significant value for researchers and engineers working in earthquake-prone countries. This article presents two case studies to demonstrate the applicability and effectiveness of the proposed framework. The first case study focuses on selecting a subset of earthquake records from a suit that meets the ASCE 7–22 requirements for NRHA on base-isolated structures, aiming to achieve the close mean responses between the full suit and the subset of records. The second case study highlights the development of an ANN model for response estimation of such structures using the proposed framework to select suitable earthquakes as the training dataset, hence providing an adequate database to achieve high estimation results. In general, the study results highlight the capabilities of the proposed frameworks and the benefits of the K-means unsupervised clustering approach in addressing the gap in the literature and providing a robust method for earthquake record selection in various analysis scenarios.

Time-frequency analysis of nonlinear structures under nonstationary excitation by directly solving structural dynamic equation through absolute displacement

The time-frequency evolution of seismic ground motion energy under strong earthquakes, which can be described by the evolutionary power spectral density (EPSD) matrix, will amplify the most unfavorable responses of members in nonlinear structural systems. However, the existing general finite element software fails to reduce the dimension of the EPSD matrix and then decouple time from frequency in frequency domain analysis. This failure greatly limits the simulation and calculation of multi-dimensional nonlinear structures with multiple degrees of freedom by the stochastic vibration theory. In this study, the pseudo excitation method (PEM), which can direct solve structural dynamic equations using absolute displacement, is used to derive the self-spectral and cross-spectral densities of seismic ground motions in one-dimensional and multi-dimensional cases. In MATLAB, the EPSD matrix is transformed into a four-dimensional uniform modulation excitation matrix independent of the time variable. Nonlinear iteration is conducted and the precise integration method (PIM) is employed through a transient analysis module. Furthermore, a simple one-dimensional example is presented to verify the correctness of the proposed algorithm herein. Finally, as an example, we select important parameters of the coherence model at different supports of a half-through three-span concrete-filled steel tubular (CFST) tied-arch bridge in view of real engineering conditions, and calculate the time-varying power spectrum and variance of the responses of arch ribs, arch feet and the bridge deck system. The results show that the theoretical derivation and the algorithm constructed in this paper can simulate the time-delay effect of the nonlinear structural system. This proves the feasibility of general finite element software in solving and analyzing random responses to multi-dimensional and multi-support non-stationary excitation of nonlinear structures.

A damage constitutive model for consistent description of static and fatigue behaviors of ultra-high performance concrete containing coarse aggregate

A suitable constitutive model for describing the damage behavior of ultra-high performance concrete (UHPC) under various loading histories plays a vital role in analyzing its structural performance. In this work, a consistent elastoplastic damage model is developed for UHPC containing coarse aggregate (UHPC-CA) subjected to static and fatigue loads, in which the driving and alleviating effects induced by the inclusions of coarse aggregate and steel fiber are considered. For damage evolution, based on the acting mechanism of the non-uniformity of stress wave propagation determined by the loading rate on the mechanical responses of UHPC-CA, the loading rate is skillfully integrated into the damage evolution rule to achieve the consistent description of mechanical behaviors of UHPC-CA under static and fatigue loading conditions. Regarding plasticity growth, an empirical plastic deformation model is adopted to improve the computational efficiency of structural nonlinear analysis. To verify the applicability of the proposed model, a user-defined UMAT subroutine is further developed for the subsequent numerical implementation. The comprehensive comparisons between the numerical predictions and independent experimental results at both the material level and structural level solidly demonstrate the capacity of the consistent model to capture the main features concerning the mechanical performance of UHPC-CA subjected to different loading paths.

Reduced-order modeling and solution method for nonlinear frequency response analysis of large space truss structures

Reduced-order modeling and solution method for nonlinear frequency response analysis of large space truss structures

Modification of wavelet-based downsampling method to reduce computational error in nonlinear dynamic analysis

One of the significant obstacles in conducting linear and non-linear time history analysis is its time-consuming nature. In this article, a new downsamlping method based on discrete wavelet transform (DWT) and smoothing is proposed to overcome this problem. In order to assess the precision of this approach, 50,000 linear and non-linear dynamic analyses of single degree of freedom (SDOF) systems and 300 nonlinear dynamic analyses of frame structures have been performed. One hundred Fema440 records were utilized to generate approximate waves up to the third level and the outcomes of this method were then contrasted with those of DWT. It has been demonstrated that the third-level approximate wave produced by DWT, previously considered dependable in other research, generates significant errors in results and the average error (absolute error percentage of the acceleration spectrum) of its third-level approximate wave is approximately 17.5%. On the other hand, the proposed method generated approximate waves with an average error of less than 4.5% across all behavior coefficients and periods and the error rate decreases as the period and behavior coefficient increase. Analysis of steel moment-resisting frames indicated that the lowest error in both methods is achieved for the base shear and across different engineering demand parameters, the average error rate for the proposed method was below 7.5%. Furthermore, caution must be exercised when employing the proposed method for structures with periods shorter than 0.5 s.

A Novel Approach to Linear and Nonlinear Time-History Analysis of Structures: Gauss–Lobatto–Hermite 4-Point (GLH-4P) Method

AbstractAn efficient time integration scheme has been devised for conducting time-history dynamic analysis of single-degree-of-freedom (SDOF) structural systems. The developed scheme belongs to Runge-Kuta family. The primary innovation of the new formulation lies in the constructive cooperation between the Hermite interpolation and the Gauss–Lobatto integration, linked to address the second-order ordinary differential equation of motion (DEOM). To put the idea into practice, several Hermite interpolators are generated to exploit the information of the internal points of Gauss-Lobatto integrator. The 4-point Gauss–Lobatto formula is employed to numerically integrate acceleration and velocity functions. This novel methodology has been designated the Gauss–Lobatto–Hermite 4-point (GLH-4P) method. GLH-4P furnishes a generally applicable implicit algorithm for conducting both linear and nonlinear analyses of structures subjected to seismic excitation. The advantage of the proposed algorithm over the conventional techniques is its higher accuracy level. Besides, it offers better stability compared with the conventional methods such as the Newmark-β and Wilson-θ methods. Unlike the other methods, GLH-4P can handle high-frequency systems without reducing the step size. Numerical examples reveal the efficacy of the GLH-4P method when juxtaposed against existing methodologies.

Truncating ground motions using the VMD-Hilbert transform for nonlinear dynamic analyses

Nonlinear dynamic analyses of engineered structures under long-duration ground motions usually require significant computational time, especially when performing incremental dynamic analyses or when developing fragility curves. This study proposes a truncation method of seismic records to reduce the computation cost of nonlinear structural analyses based on the Variational Mode Decomposition and the Hilbert Transform. The truncation-starting and -ending time instants are identified using the relative cumulative spectral energy, which is used to represent the Hilbert spectrum energy variation over time. The effectiveness of the proposed method is verified by the elastic pseudo-response spectrum, three different inelastic single-degree-of-freedom models and a multi-degree-of-freedom system. The proposed method, compared with the Arias intensity-based method, proves to be effective, not only for short-period structures, but also for medium- and long-period structures, allowing for reduction of ground motion duration of about 65% on average.

Performance of coal gangue concrete with fly ash and ground-granulated blast slag: Rheology, mechanical properties and microstructure

This paper aims to examine the effect of coal gangue aggregate (CGA), fly ash (FA), and ground-granulated blast slag (GGBS) on the rheological, mechanical and microstructure properties of concrete. The rheological properties, compressive strength, splitting tensile strength, flexural strength, and uniaxial tensile behaviour of coal gangue concrete (CGC) were determined, and the microstructure of the concrete mixtures were investigated by use of XRD and SEM analyses. The results revealed the action mechanism of CGA and mineral admixtures on the microstructure and macroscopic properties of CGC. FA first increased and then decreased the yield stress and plastic viscosity, while GGBS considerably increased the yield stress and plastic viscosity. Furthermore, a constitutive model was established for CGC containing FA and GGBS under compression. The proposed stress–strain model for CGC is accurate and can be used for nonlinear analysis of structures made of this type of concrete. Moreover, the addition of FA and GGBS consumes calcium hydroxide, but increases products such as hydrated calcium silicate aluminate. These findings elucidate the understanding and optimisation of CGA use in concrete production, while contributing to lowering carbon emissions.

Correction to: Optimized Gauss–Legendre–Hermite 2-point (O-GLH-2P) method for nonlinear time-history analysis of structures

Correction to: Optimized Gauss–Legendre–Hermite 2-point (O-GLH-2P) method for nonlinear time-history analysis of structures

Design parameter study based on nonlinear analysis of a bolt-connected precast concrete composite wall panel structure

Design parameter study based on nonlinear analysis of a bolt-connected precast concrete composite wall panel structure

Accurate non-linear bending analytical solutions setting new benchmarks for rectangular thin plates with four simply supported edges

In the field of nonlinear structural analysis, the ability to provide accurate and reliable analytical solutions is of paramount importance. This paper presents more accurate nonlinear analytical solutions for rectangular plates with four simply supported edges, establishing a new benchmark that replaces and complements Lévy’s manual analytical solutions. These accurate solutions can serve as a reference for validating various nonlinear numerical and approximate analytical solutions, thereby providing a robust basis for engineering design. Notably, the central deflection error in this study is less than 0.005%, while the central stress error remains below 0.4%. The accuracy of the present solutions provided significantly exceeds that found in the existing literature.

Nonlinear dynamic collapse analysis of space semi-rigid frames using finite particle method

Based on the finite particle method, this work presents a general numerical method to perform the nonlinear dynamic collapse analysis of space semi-rigid structures. A space connection element composed of two particles and six zero-length springs is proposed to simulate the space semi-rigid connection. Geometrical nonlinearity is addressed through fictitious motion, while material and connection behavior nonlinearities are captured by updating the element stiffness matrix and the connection stiffness matrix, respectively. Member and connection fracture models are convenient for simulating fracture behaviors during collapse processes. To verify the effectiveness of the proposed method, the numerical results are compared with those from previous studies, and energy conversion analyses are adopted. The analysis results indicate that only member fractures occur at beam ends in the rigid and linear semi-rigid frames, while only connection fractures occur at beam ends in the nonlinear semi-rigid frame.

Nonlinear Analysis of Building Structures Resting on Soft Soil Considering Soil–Structure Interaction and Structure–Soil–Structure Interaction

Nonlinear Analysis of Building Structures Resting on Soft Soil Considering Soil–Structure Interaction and Structure–Soil–Structure Interaction

Numerical simulation of the 2010 4-story reinforced concrete structure tested on the E-defense shake table

Due to advancements in computational tools, performing a full nonlinear response history analysis of structures at the system level using detailed numerical simulations of components has become less demanding, even on standard personal computers. However, the modelling approaches need to be calibrated and verified against experimental measurements to ensure the accuracy of the system-level predictions. In this study, an advanced numerical simulation method is used to predict the 3D nonlinear dynamic response of a four-story reinforced concrete building tested at E-Defense shake table. The structure is modelled in the finite element analysis programme DIANA, using a previously developed and validated approach to predict the failure modes of doubly reinforced walls with confined boundary regions. Curved shell elements are used to model the walls and slabs, and the reinforcement is modelled using embedded bar elements. The frame elements are modelled using beam elements with the effect of confinement on the concrete behaviour represented in the material constitutive model. The numerical versus experimental response comparison is conducted at both local and global levels. For local levels, the base shear versus top displacement curves, strain gradients as well as the crack pattern predicted by the numerical model are compared with the test measurements. The inter-story drift response history is considered as the metric for the global level assessment. The effects of different modelling parameters on the accuracy of predictions are also investigated.

Non-Linear Behaviour and Analysis of Innovative Suspension Steel Roof Structures

Suspension structures are one of the most effective roof load-bearing structures for medium to long spans. Their shape under symmetric loads is usually a square parabola or a curve close to it. The biggest drawback of such structures is their increased deformability under asymmetric loads. So-called rigid cables are used to solve this problem. However, the production of such rigid cables with a curvilinear shape is complicated, and their maintenance also has drawbacks due to the above-mentioned shape. To avoid these shortcomings, straight-line suspension structures have been used. This paper proposes a new form of combined suspension roof structures consisting of main load-bearing straight suspension elements supported by cable struts. For the main suspension elements, the bending stiffness is accepted, taking into account the operational requirements of the structure. This article analyses the behaviour of such a combined suspension structural system in symmetric conditions with an innovative approach. The arrangements of this system are discussed. The calculation of the forces and displacements of this structure and its elements is presented, taking into account the geometrical nonlinear behaviour. The distribution of the forces in the rigid elements and node displacements of the structure are discussed. The proposed new form of a combined cable-supported roof structure was shown to be more effective in terms of weight than the standard parabolic-shaped suspension structure.

Nonlinear structural analysis technique based on flexibility method by Pade approximants

Nonlinear structural analysis technique based on flexibility method by Pade approximants

Some remarks on load modeling in nonlinear structural analysis–Statics with large deformations–Consistent treatment of follower load effects and load control

AbstractLoad modeling in nonlinear statics, particularly incorporating large deformations differs significantly from the treatment in linear analysis. As in structural dynamics masses in a gravity field generate the loading, their location, and their modifications within the deformation process must be considered in a nonlinear simulation. A specific view besides loading by masses is on gas and fluid interaction with structures. In addition, load control using specifically designed algorithms is evaluated with respect to realistic applications. Within the load modeling an unavoidable, however side aspect, is the general discussion about the so‐called follower forces and non‐conservative loading. As an example of real‐world applications, the specifics of inflated rubber dams are presented.

Effects of edge-crack orientation and depth on non-linear dynamics of laminated nanocomposite single-variable-edge plates

This paper presents an investigation into the free vibration and nonlinear dynamic analyses of new complex edge contour plate structures, known as single-variable-edge (SVE) plates. Cracks emerge at the center of the plate’s surface, and the effects of edge crack orientation and depth on the dynamical characteristics of the laminated nanocomposite SVE plates have been considered in this study. The functionally graded graphene nanoplatelet reinforced composite (FG-GPLRC) material was utilized for the edge-cracked plate that rests on a Winker-Pasternak elastic foundation. The Halpin-Tsai micromechanical model is used to predict the material characteristics, which are presumptively temperature-dependent. The rule of mixtures is employed to determine Poisson's ratio, density mass, and thermal expansion. The governing equations are established based on the theory of elasticity, and Von Karman-Donnell geometric nonlinearity assumption. To confirm the reliability and accuracy of this approach, the acquired findings are validated with those produced using Finite Element Analysis (FEA). Furthermore, the geometrical and material parameters, fracture properties, and environmental (temperature and elastic foundation) factors are also investigated in the study. The research findings hold significant implications for applications in aerospace and aeronautical, civil, and mechanical engineering.