Analysis Of Complex Structures Research Articles

Trifluoromethyl substituted cationic cyclometallated iridium(III) complexes: Photophysical properties and theoretical studies

Three new trifluoromethyl substituted (–CF3) cationic iridium(III) complexes 1–3, with 3,5-dimethyl-1-(3-(trifluoromethyl)phenyl)-1H-pyrazole (DTPP) as the cyclometallated ligand, namely, [Ir(DTPP)2bpy](PF6) (1, bpy = 2, 2′–bipyridine), [Ir(DTPP)2phen](PF6) (2, phen = 1,10-phenanthroline) and [Ir(DTPP)2pphen](PF6) (3, pphen = pyrazino[2,3-f][1,10]phenanthroline) have been rationally designed and synthesized in good yields (60–77%). The photophysical, electrochemical, and electroluminescent properties were fully characterized. Complexes 1–3 show bright blue to yellow emission in the both solution and neat film states with maximum emission wavelength in the range of 484–560 nm. Photoluminescence quantum yields (PLQYs) are very high ranging from 62% to 72% in the solution state with microsecond excited-state lifetimes (0.39–0.77 μs). More detailed photophysical and theortical calculation studies reveal that introduction of –CF3 substituent onto the cyclometallated ligand can induce a blue-shift emission compared with conventional fluorinated phenylpyridine or phenylpyrazole complexes, which can be contributed to the decline in HOMO energy level of complexes. Single-crystal structure analysis of complex 3 shows a distorted octahedral geometry with strong intermolecular π–π stacking (face-to-face) interactions between ancillary ligands in adjacent molecules, which might be responsible for the obviously red-shifted emission compared with complexes 1 and 2 in the aggregated state. In addition, electroluminescent properties of all three new complexes have been studied in the application of light-emitting electrochemical cells (LECs), which show green to yellow electroluminescence (λmax, EL = 516–540 nm).

Modal Analysis of a High-Speed Train Gearbox Housing Using Smoothed Finite Element Method

The gearbox is a crucial component of the power transmission system in high-speed trains, and realistically calculating its natural frequency is vital in avoiding system resonance. In recent decades, numerical techniques have become essential in designing engineering structures, and the finite element method (FEM) has gained widespread recognition and acceptance for its robustness and effectiveness. However, the FEM technique using linear 4-node tetrahedral elements (T4) performs poorly, leading to low accuracy and unreliable results. Consequently, complex hexahedral or second-order elements are often required for better performance. In this paper, we employ the smoothed finite element method (S-FEM), which combines the gradient smoothing technique with the standard FEM to improve calculation accuracy while still using linear tetrahedral elements. We apply S-FEM to accurately obtain the natural frequencies and mode shapes of a high-speed train gearbox using automatically generated linear tetrahedral elements. A test of tolerance to mesh distortion is also carried out on the gearbox. The results demonstrate that S-FEM can significantly enhance the computational accuracy of low-order 4-node tetrahedral elements without altering the mesh topology. It is expected that S-FEM can be an alternative to FEM in the modal analysis of complex structures in the railroad industry.

Acidity Quantification and Structure Analysis of Amide-AlCl3 Liquid Coordination Complexes for C4 Alkylation Catalysis

Liquid coordination complexes (LCCs), which are formed between metal halides and donor molecules, represent promising catalysts. Six amide-AlCl3 LCCs were successfully synthesized, followed by their characterization through NMR, Raman, and UV-visible spectroscopy. The acidity of these LCCs was quantified by performing computational modelling of fluoride ion affinities (FIA) and experimental Gutmann–Beckett measurements. Spectroscopic analysis indicated bidentate coordination between amide ligands and Al, which induced asymmetric splitting of Al2Cl6 into diverse ions such as [AlCl2L2]+, [AlCl4]−, [AlCl3L], and [Al2Cl6L]. The computed FIA was found to align well with the experimental acidity trends, thereby confirming the proposed structure of the LCC. In the alkylation tests, the LCC with a high acidity demonstrated an increase in the yields of C5-C7 alkylates. These results provide an in-depth understanding of the tuneable structures of amide-AlCl3 LCCs. The acidity of LCCs can be controlled by tuning the ratio of the organic ligand to AlCl3, which allows bidentate coordination to facilitate asymmetric splitting of Al2Cl6. The LCCs demonstrate a high degree of potential as versatile and sustainable acid catalysts in alkylation reactions. These findings may advance the foundational knowledge of LCCs for the purpose of targeted acid catalyst design.

Synthesis, crystal structure and Hirshfeld surface analysis of a cadmium complex of naphthalene-1,5-di-sulfonate and o-phenyl-enedi-amine.

A novel o-phenyl-enedi-amine (opda)-based cadmium complex, bis-(benzene-1,2-di-amine-κ2 N,N')bis-(benzene-1,2-di-amine-κN)cadmium(II) naphthalene-1,5-di-sulfonate, [Cd(C6H8N2)4](C10H6O6S2), was synthesized. The complex salt crystallizes in the monoclinic space group C2/c. The Cd atom occupies a special position and coordinates six nitro-gen atoms from four o-phenyl-enedi-amine mol-ecules, two as chelating ligands and two as monodentate ligands. The amino H atoms of opda inter-act with two O atoms of the naphthalene-1,5-di-sulfonate anions. The anions act as bridges between [Cd(opda)4]2+ cations, forming a two-dimensional network in the [010] and [001] directions. The Hirshfeld surface analysis shows that the primary factors contributing to the supramolecular inter-actions are short contacts, particularly van der Waals forces of the type H⋯H, O⋯H and C⋯H.

A novel adaptive Kriging method combining Hessian matrix and an efficient F-scoreβ-based stopping criterion for structural reliability analysis

Reliability analysis of complex structures or highly nonlinear performance functions generate an enormous computational burden and affects computational efficiency. It is crucial to accurately assess structural reliability. However, current methods do not meet the accuracy and efficiency requirements as the complexity and nonlinearity of the model gradually increase. To address these problems, a novel active learning Kriging method combined with a Hessian matrix was proposed for efficient structural reliability analysis. The predicted mean of the Kriging model was used as an element of the Hessian matrix to describe the degree of nonlinearity of the model. Based on the fact that the iterative process is greatly influenced dramatically by the sample points in proximity to the limit state surface (LSS), a candidate sample pool (CSP) is generated, where the sample points located in the vicinity of the LSS with a larger curvature are chosen to add to the design of experiments (DoE). A stopping criterion about F-scoreβ based on the number of the misclassified points is proposed to judge the model fitting effect, which can be used to effectively identify the LSS. Two mathematical cases and two finite element cases were used to illustrate the high accuracy and efficiency of the method, which a novel manner of the nonlinear reliability calculation is provided.

Electronic structure analysis of phthalocyanine complexes using magnetic circular dichroism and magnetic circularly polarized luminescence spectroscopy.

In the study of phthalocyanine complexes using magnetic circular dichroism (MCD) spectroscopy, the electronic structure of excited states is generally discussed based on the rigid-shift approximation, in which the band profiles for left-handed circularly polarized (lcp) and right-handed circularly polarized (rcp) light are assumed to be the same. This assumption may not necessarily be valid for cases where there are multiple initial states having different geometries. Magnetic circularly polarized luminescence (MCPL) from phthalocyanine complexes can be regarded as an example of such cases, since the two degenerate emission states are split in a magnetic field and can undergo a structural deformation. Here, we investigated an alternative approach, where the lcp and rcp components are independently determined. This method, which we refer to as the direct-separation approach, allows direct determination of the distribution of the two emission states as well as the orbital angular momentum . Using this approach, and the distribution were determined from MCD and MCPL spectra of a series of phthalocyanine complexes. Comparison of the two methods shows that the rigid-shift and the direct-separation approaches give practically equivalent results for the systems under study, but the latter is advantageous for systems where the former is not applicable.

Deep learning classifier for life cycle optimization of steel–concrete composite bridges

The ability to conduct life cycle analyses of complex structures is vitally important for environmental and social considerations. Incorporating the life cycle into structural design optimization results in extended computational durations, underscoring the need for an innovative solution. This paper introduces a methodology leveraging deep learning to hasten structural constraint computations in an optimization context, considering the structure’s life cycle. Using a composite bridge composed of concrete and steel as a case study, the research delves into hyperparameter fine-tuning to craft a robust model that accelerates calculations. The optimal deep learning model is then integrated with three metaheuristics: the Old Bachelor Acceptance with a Mutation Operator (OBAMO), the Cuckoo Search (CS), and the Sine Cosine Algorithms (SCA). Results indicate a potential 50-fold increase in computational speed using the deep learning model in certain scenarios. A comprehensive comparison reveals economic feasibility, environmental ramifications, and social life cycle assessments, with an augmented steel yield strength observed in optimal design solutions for both environmental and social objective functions, highlighting the benefits of meshing deep learning with civil engineering design optimization.

Volumetric embedded entities for the IsoGeometric Analysis of complex structures

We propose a convenient methodology for the modeling and analysis of aircraft compressor blades. To meet this goal, IsoGeometric Analysis is put to good use, as it allows for an exact representation of the geometry, especially for the analysis. This work aims at developing numerical tools to handle mechanical analysis, and later on shape optimisation, of 3D aircraft engine compressor blades using IGA. More precisely, our final goal is to carry out shape optimisation of one precise patch belonging to a complex multipatch structure, while having other patches to follow automatically the geometric changes. To meet this goal, work on geometric and modeling aspects are needed, which is the objective of this paper. Using the proposed techniques to perform gradient-based shape optimisation constitutes a work in itself and is therefore not presented here, but will be detailed in a follow-up paper.In our case, the complete blade assembly is represented using several volumetric patches: the airfoil, the platform, the tenon and the fillet. In order to ensure the geometric compatibility between the different patches, we propose an embedded solid element formulation. A mortar method is implemented in order to guarantee the coupling between the various parts of the assembly. The results show a great potential for the proposed approach for blades design, while concurrently offering broad perspectives in terms of applications.

Galeite, Na15(SO4)5ClF4, and Schairerite, Na21(SO4)7ClF6: Phase Transitions, Thermal Expansion and Thermal Stability

In this study, galeite, Na15(SO4)5ClF4 and schairerite, Na21(SO4)7ClF6 were investigated via in situ single-crystal X-ray diffraction in the temperature range of 300–750 K. Galeite and schairerite are trigonal, P31m, a = 12.1903(2), c = 13.9454(2) Å, V = 1794.69(6) Å3, and Z = 3 (R1 = 0.0273, 300 K) for galeite and a = 12.1859(3), c = 19.3080(6) Å, V = 2483.04(14) Å3, and Z = 3 (R1 = 0.0334, 300 K) for schairerite. The crystal structures of galeite and schairerite are based upon frameworks consisting of alternating face- and corner-sharing fluorine- and chlorine-centered octahedra. Galeite and schairerite can be attributed to 5H (galeite) and 7H (schairerite) antiperovskite polytypes, respectively. It was observed that schairerite undergoes at least one reversible phase transition before it starts to lose its crystallinity at 750 K. This phase transition occurs in the temperature range of 550–600 K. The high-temperature modification of schairerite is trigonal, with the centrosymmetric space group P-3m1 and the unit-cell parameters a = 7.0714(2), c = 19.5972(7) Å, V = 848.66(6) Å3, and Z = 1. Galeite is stable up to 600 K. The crystal structures of minerals expand anisotropically, and, in both cases, the strongest thermal expansion was parallel to the modules of face-sharing anion-centered octahedra. The structural complexity analysis showed that galeite is complex (695.175 bits/cell) and that the LT-modification of schairerite is very complex (1064.990 bits/cell), whereas its HT-modification is intermediate in complexity (256.755 bits/cell). The complexities of LT- and HT-polymorphs of schairerite are consistent with the general observations regarding structures with positional disorder: complexity decreases with increasing temperature, and simpler polymorphs have lower physical density.

Ni(II) complexes with in-situ generated N, O-bidentate aroylhydrazone Schiff base ligands: One-pot synthesis, characterization, crystal structure, and in-silico studies

A series of novel aroylhydrazone-based Ni(II) complexes were synthesized by using analogous Schiff base ligands prepared in-situ by reacting 4-[(4-methylbenzyl)oxy]benzoylhydrazine with different aldehydes in the presence of Ni(II) acetate tetrahydrate. The correspondent [NiL2] complexes, 4-7, were characterized by physicochemical techniques, viz., molar conductance, magnetic susceptibility measurement, IR, NMR, and mass spectroscopic techniques. The single-crystal X-ray structural analyses of complexes 4, 6 and 7 showed a distorted square-planar geometry for Ni atoms with deprotonated ligands in trans-configuration bound via azomethine-N and carbonylate-O atoms. Next, quantum chemical methods were incorporated to investigate their thermochemical, molecular orbital, and electrostatic potential properties. Computer-aided drug design methods were also implemented to assess their medicinal, pharmacological, and toxicological properties. Molecular docking and interaction analyses disclosed their potential binding affinity against human lung Cytochrome P450 2A13 receptor protein. Pharmacokinetic and toxicological studies suggest their relatively safe drug administrative properties.

Kabirian-based optinalysis: A conceptually grounded framework for symmetry/asymmetry, similarity/dissimilarity and identity/unidentity estimations in mathematical structures and biological sequences

This paper introduces “Kabirian-based optinalysis (KBO),” a pioneering framework that addresses the longstanding challenges in estimating symmetry/asymmetry, similarity/dissimilarity, and identity/unidentity within mathematical structures and biological sequences. The existing methods often lack a strong theoretical foundation, leading to inconsistencies and limitations. Kabirian-based optinalysis draws inspiration from isomorphism and automorphism, providing a theoretically grounded framework that unifies estimation methodologies. It introduces the concept of optiscale, autoreflective pairing, isoreflective pairing, and others ensuring invariance and robustness under various mathematical transformations and establishing functional bijectivity for isomorphic or automorphic structures. This not only overcomes previous limitations but also offers precise and interpretable estimations. Additionally, the framework introduces “geometrical pairwise analysis” to improve sensitivity to position-specific and character-specific variations in biological sequences. This novel approach enhances the accuracy of sequence similarity assessments, surpassing the constraints of conventional methods. The novelty of this work extends beyond mathematics and biology, impacting diverse fields such as computer science, data analysis, pattern recognition, and evolutionary biology. Kabirian-based optinalysis presents a holistic and theoretically grounded solution that has the potential to revolutionize the analysis of complex structures and sequences, opening new horizons for interdisciplinary research.•Inspired by automorphism and isomorphism, Kabirian-based optinalysis introduces a new paradigm-shifting and unified approach to estimations in mathematical structures and biological sequences with a solid conceptual and theoretical foundation.•The GPA method enhances pairwise sequence similarity estimation by being sensitive to position-specific and character-specific variations and providing a comprehensive characterization of these features.

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.

Powder crystal structure analysis of salen metal complexes with phenylalkyl groups

Powder crystal structure analysis of salen metal complexes with phenylalkyl groups

Theatre art: Conceptual and categorical problems

Theatre art is a fundamental component of modern culture and requires a detailed analysis of the problems of a set of interrelated concepts, which will reflect the key substantive and functional aspects concerning theatre art. The research relevance is determined by the description of the problems of the conceptual and categorical apparatus of theatrical art for the first time is subjected to a complex structural and semantic analysis, which is necessary to determine the study of ways of forming new terms, which will make it possible to present the system of modern theatrical terminology in a holistic form. The study aims to analyse and describe the contemporary problems of the conceptual and categorical apparatus of theatrical art. General scientific methods of art history were used: method of analysis, comparative analysis, synthesis, analogy, and classification. The article investigates the whole stage space as one of the components in the context of the conceptual categorical apparatus of modern art history. Contemporary theatre art is undergoing an active evolution, with artists striving for innovation, using interactive elements, multimedia technology and art installations to create a deep and rich experience for the audience. An important aspect is to involve the viewer in the experience, where the traditional boundaries between actors and audience are blurred and the viewer becomes an active participant. Theatres also emphasise diversity, aiming to reflect different cultures and identities on stage. However, there are problems with the conceptual and categorical apparatus, requiring the development of new terms to accurately describe contemporary phenomena in theatre. Sarcasm and irony prevail, artists seek new directions, and all this happens in the context of the diversity of theatre traditions, creating challenges in the exchange of experiences between cultures. The materials discussed in this article can be applied by both theorists and practitioners of contemporary art history in their writings and as material for teaching in the educational process when training specialists in the field of contemporary art

Mining and geological models of virtual complex ore blocks of the bench

Purpose. Creation of mining and geological models of virtual complex ore blocks of a bench to develop a basic methodology for determining the geological structure of complex structural sections of mineral deposits. Methodology. In the scientific and technical substantiation of mining and geological, mining and technical indicators of complex structural blocks in terms of ore saturation and complexity of the morphological structure of blocks of ledges, methods of complex and abstract-logical analysis, synthesis, systematization, the method of theoretical generalization, generalization of information sources and world experience in the field of geoinformation of complex structural deposits, statistical analysis, mathematical modeling, mining and geological modeling of mineral deposits were applied. Findings. Mining and geological models of virtual complex structure ore blocks (CSOB) of the bench have been created. The mining and geological characteristics of the blocks are analytically interconnected with the geometric parameters of the scattered ore bodies and the dimensions of the layer of admixed rock or lost ore. They determine the degree of complexity of the geological structure of the CSOB. According to the given sizes and location of disparate solid and dispersed ore bodies of virtual complex structural blocks, the numerical values of the mining and geological characteristics of ore blocks were calculated using the developed method. CSOB are subdivided into more ore-saturated, moderately ore-saturated, less ore-saturated as well as complex structural and more complex structural ones. Originality. For the first time in mining, the concepts of “virtual complex-structural ore blocks of a bench” and “mining and geological models of virtual complex-structural ore blocks of a bench” have been introduced. The set of geometrical parameters of the scattered ore bodies of the block and their mining and geological characteristics are presented as mining and geological models of the virtual CSOB of the bench. The developed models make it possible to establish patterns of changes in the mining and geological characteristics of complex ore blocks. Practical value. The developed mining and geological models of virtual complex structural blocks serve as the basis for creating mining and geological models of real complex ore blocks, models of CSOB in a blasted state. They will make it possible to develop a methodology for rationing losses and impoverishment of ores for real complex-structural blocks, to choose rational parameters for mining technologies for disparate ore bodies in specific mining and geological conditions, and to expand the use of waste-free, low-waste technologies in the development of complex-structural mineral deposits.

A comprehensive review on estimation of equivalent static wind loads on long-span roofs

Equivalent static wind load (ESWL) is helpful information for designing wind-sensitive structures since it converts complex wind-induced structural dynamic analysis into a simplified static analysis and facilitates combination of other loads or actions in structural designs. In recent years, there have been a growing number of long-span roof structures, most of which are sensitive to wind actions. Indeed, the accurate determination of ESWLs has been a primary concern in their wind-resistant design. Although some significant progress has been made on this topic, there are various issues to be addressed or improved due to a variety of reasons. With the further development of long-span roofs, there will be higher requirements for their ESWLs. This paper first combs through the existing representative methods depending on wind-induced structural responses (WISRs) and wind-induced structural stability (WISS), where the ESWLs linked with the former are the mainstream and the ones concerned with the latter are still somewhat in their initial stages of development. In each broad category, some momentous tactics of mathematics and mechanics are utilized to derive different methods. In the conclusion, this paper finally summarizes the existing achievements, highlights the technical challenges that hinder the current methods from being widely adopted and proposes some latent solutions for the future research. This review paper is anticipated to be a comprehensive reference for researchers and professionals in this field of study.

A RBFNN based active learning surrogate model for evaluating low failure probability in reliability analysis

This paper presents a novel active learning surrogate model for estimating low failure probability in the reliability analysis of complex structures based on a radial basis function neural network (RBFNN). The RBFNN surrogate model, which possesses global approximation capability, is constructed by randomly selecting an initial design of experiments (DoEs) from a Monte Carlo Simulation (MCS) population using the minimax distance method. Furthermore, the RBFNN surrogate model is updated by sequentially adding highly representative samples to improve the local prediction accuracy. The highly representative samples are selected using minimax distance method from each level’s failure region of subset simulation (SS), and are further modified by the calculation of actual limit state function (LSF). Consequently, the low failure probability is obtained through an iterative framework that combines SS and RBFNN surrogate model. The proposed approach significantly reduces the number of experiments required, resulting in lower costs and higher efficiency. Three examples are provided to demonstrate the effectiveness and accuracy of the proposed method.

An efficient time-variant reliability analysis strategy embedding the NARX neural network of response characteristics prediction into probability density evolution method

Stochastic response analysis and first-passage reliability evaluation of multi-degree of freedom nonlinear systems subject to non-stationary seismic excitation have been a critical issue in the field of compound random vibrations, yet remain unsolved. This study extends the time-varying reliability analysis method based on the probability density evolution method, making it applicable to the problem of stochastic response analysis and first-passage reliability evaluation of complex engineering structures. To efficiently represent the response of representative samples, a nonlinear autoregressive with exogenous inputs neural network model is introduced in this study. After comparing three different optimization methods, the neural network model based on the Bayesian regularization algorithm is selected as the predictor for the response of complex nonlinear systems, enabling efficient stochastic response analysis and time-varying reliability evaluation. To this end, leveraging the high efficiency of the probability density evolution method, the analysis of time-varying reliability of large-scale structures has been successfully conducted. Furthermore, the proposed method can be easily expanded to dynamic reliability evaluation problems represented by extreme value theory. Three numerical examples are quoted to demonstrate the applicability and advantages of the proposed method in the field of first-passage and extreme-value problems of systems, which are also compared with PCE, SVR, and Kriging. The results from these numerical examples indicate that the proposed method can effectively reduce the required calculational cost for the reliability analysis of complex structures while maintaining high analytical accuracy.

Reliability Evaluation of a Nonlinear Frame Structure under Explosive Ground Motions Generated by Dimension-Reduction Method

In the present study, a stochastic model of explosive ground motions applying the dimension-reduction method is proposed, and the reliability evaluation of a nonlinear frame structure under such excitations is realized by means of the probability density evolution method and an equivalent extreme-value-based reliability evaluation strategy. Firstly, the evolutionary power spectrum density function of the explosive ground motions is modeled by respectively identifying the normalized total energy distribution function and the frequency total energy distribution function on the basis of the measured motion records. In addition, an exponential model is constructed to forecast the seismic characteristics of the explosive ground motions based on the given distance to the explosive source and the charge quantity. Then, the representative samples of the explosive ground motions are simulated using the dimension-reduction method. The simulation results show that the generated acceleration samples have significant seismic characteristics of the explosive ground motions, and the accuracy is verified by comparing the second-order statistics with the sample set and the corresponding targets. Due to the fact that the probabilities of the representative samples simulated by the dimension-reduction method can compose a comprehensive probability set, it contributes to the refined dynamic response analysis and reliability evaluation of complex structures combining with the probability density evolution method. The accurate dynamic response analysis and reliability evaluation of a nonlinear frame structure illustrates the effectiveness of the proposed model and the dimension-reduction method for simulating the explosive ground motions. The numerical results demonstrate that the explosive ground motions have a substantial effect on the nonlinear behavior and the security of engineering structures.

A dynamic Gaussian process surrogate model based on the grasshopper optimization algorithm for non-probabilistic reliability analysis of complex structures

In practical complex engineering structures, the performance function (PF) for reliability analysis is commonly implicit and highly nonlinear. Commonly used surrogate models are appropriate for structural reliability analysis with an implicit PF. However, these methods require hundreds of PF values, which are time-consuming to obtain by adopting numerical analysis, such as finite element analysis (FEA). Therefore, since non-probabilistic reliability analysis does not require a large number of samples, it has great development potential. In this paper, a dynamic Gaussian process (GP) surrogate model based on the grasshopper optimization algorithm (DGP-GOA) is proposed for the non-probabilistic reliability analysis. First, with the help of the scale factor of the convex set model, the non-probabilistic reliability analysis problem is transformed into an unconstrained optimization problem. Second, the DGP-GOA fits the PF by constructing a GP surrogate model with a small dataset. Third, the GOA is used to search for the global optimal solution to obtain a non-probabilistic reliability index. Then, a dynamic retraining strategy is proposed to improve the fitting accuracy and efficiency. The results demonstrate that the proposed method is highly applicable to the non-probabilistic structural reliability analysis of complex engineering structures.