Nonlinear dynamic co-rotational formulation for membrane elements with in-plane drilling rotational degree of freedom

This chapter focuses on the applications of the quadrilateral area coordinate systems discussed in the pre vious chapter. Here, a series of new quadrilateral elements formulated by the quadrilateral area coordinate methods are introduced in detail. Foll’ owing the Introduction in Sect. 17.1, the sensitivity analysis of the quadri lateral membrane elements to mesh distortion is discussed in Sect. 17.2. Then, a brief review of the construction of various quadrilateral elements formulated by the quadrilateral area coordinate methods is given in Sect. 17.3. In Sects. 17.4 to 17.7 of this chapter, various quadrilateral membrane elements (4-node element, 4-node element with drilling freedoms, 8-node element) for linear and nonlinear analyses, in which the are coordinate methods are adopted, are introduced in detail. And, in the last three sections (Sects. 17.8 to 17.10), the applications of the area coordinate methods for the quadrilateral thin plate, thick plate and composite laminated plate elements are descri bed, respectively. It is demonstrated that the area coordinate methods are efficient tools for developing simple, effective and reliabl e serendipity quadrilateral element models.

Application of the endurance time methodology on seismic analysis and performance assessment of hydraulic arched tunnels

Based on the linear superposition of the quadrilateral isoparametric membrane element and quadrilateral Mindlin plate element, basic vector formulas for the quadrilateral isoparametric shell element with the shear deformation is derived. Two different coordinate modes for updating the particle displacement and the element node internal force are put forward. The uniform numerical solution for an irregular quadrilateral element is realized by the isoparametric integral scheme along the element plane. Then, the bilinear elastoplastic constitutive of material is introduced into the vector finite shell element, and the nonlinear effect of the material is realized based on the integral method along the thickness. On this basis, the nonlinear calculation and analysis program of the quadrilateral isoparametric shell element is developed. Numerical example results show that the static and dynamic analysis, large deformation and large rotation analysis, and buckling analysis can all be well performed for the shell structures by the developed program, which verifies the validity of theoretical derivation and computer program.

An assessment is made of a 4‐node quadrilateral membrane element with one rotational and two translational degrees of freedom per node, as formulated by Taylor and Simo. The element, QC9, is formed by degeneration of the 9‐node Lagrange element and condensation of the centre degrees of freedom. An 8‐point, modified reduced integration scheme is implemented in this element, QC9(8), to improve on the 3 × 3 quadrature performance, yet avoid the additional rank deficiency due to reduced integration (2 × 2). QC9(8) performs as good or better than all elements surveyed. It is shown that a similar degeneration of the 16‐node Lagrangian element can be carried out, but that the resulting element fails the patch test.

Drape simulation using solid-shell elements and adaptive mesh subdivision

Importance of ‘DAF’ in evaluating structural adequacy of gravity-load designed RC buildings

The structural analysis involves the definition of the model and selection of the analysis type. The model should represent the stiffness, the mass, and the loads of the structure. The structures can be represented using simplified models, such as the lumped mass models, and advanced models resorting the finite element method (FEM) and discrete element method (DEM). Depending on the characteristics of the structure, different types of analysis can be used such as limit analysis, linear and nonlinear static analysis, and linear and nonlinear dynamic analysis. Unreinforced masonry structures present low tensile strength, and the linear analyses seem to not be adequate for assessing their structural behavior. On the other hand, the static and dynamic nonlinear analyses are complex, since they involve large time computational requirements and advanced knowledge of the practitioner. The nonlinear analysis requires advanced knowledge on the material properties, analysis tools, and interpretation of results. The limit analysis with macro-blocks can be assumed as a more practical method in the estimation of maximum load capacity of structure. Furthermore, the limit analysis requires a reduced number of parameters, which is an advantage for the assessment of ancient and historical masonry structures, due to the difficulty in obtaining reliable data. The observation of the damage in masonry buildings caused by earthquakes in the past has been shown that the masonry structures can be discretized into several macro-blocks and interfaces. The macro-blocks are portions of a structure with similar material properties and structural behavior, to which the mechanical properties of the material can be assigned or, by simplification, they can be assumed to be infinitely rigid. The interfaces in a macro-modelling represent, in general, the cracks associated to the failure mechanisms. However, in a micro-modelling strategy applied to masonry, in which the units and the joints are individually considered, the interfaces simulate the behavior of the joints. Furthermore, different criteria for the strength parameters of macro-blocks and interfaces can be considered. The limit analysis (Fig. 1) with macro-blocks is a simplified and powerful structural analysis tool to evaluate the ultimate capacity of masonry structures by static models, involving the equilibrium of the macro-blocks through the limit analysis basic concepts.

Determination of dynamic collapse limit states using the energy-based method for multi-story RC frames subjected to column removal scenarios

This study is the compared seismic performance that are difference between the performance of structures on various site classes and beam-column connection. this analysis model was designed the previous earthquake load. To compare the performance levels of the structure was subjected to nonlinear static and nonlinear dynamic analysis. Nonlinear analysis was used to The Perform 3D program. Nonlinear static analysis was compared with the performance point and Nonlinear dynamic analysis was compared the drift ratio(%). Analysis results, the soft site class of the displacement was more increase than rock site classes of the displacement. Also The smaller the displacement was increased beam-column connection stiffness.

When applied finite element method to numerical simulation, the discretization of the domain is essential part of the procedure. There are few reports about the quadrilateral mesh generation method in comparison with triangular mesh generation. The characteristic of the proposed algorithm is that the quadrilateral of the inner nodes is carried out by bucket method in computational geometry. And then the triangulation of the residual region is carried out utilizing advansing front method. Therefore the mixed elements of triangular and quadrilateral elements are generated in this step. In the next step, a quadrilateral element is constructed connecting two triangular elements with a common side. Finally, the quadrilateral elements are generated by the subdivision of the mixed elements. The processing scheme is developed and applied to several examples.

Given the vast advancements in computing power in the last several decades, nonlinear dynamic analysis has gained wide acceptance by practicing engineers as a useful way of assessing and improving the seismic performance of structures. Nonlinear structural analysis software packages give engineers the ability to directly model nonlinear component behavior in detail, resulting in improved understanding of how a building will respond under strong earthquake shaking. One key component, in particular, for understanding the behavior of moment-resisting frames is the plastic rotation of the flexural hinges. Performance-based standards typically use plastic rotation as the primary parameter for defining the acceptance criteria in moment-resisting frames. Since plastic rotation is a key parameter in the seismic damage assessment, the concept as well as the method to calculate this quantity must be understood completely. Though engineers rely on the plastic rotation output from seismic structural analysis software packages to determine acceptable performance, the actual calculation methods used in achieving such plastic rotation quantities usually lay within a so-called “black box”. Based on the outputs obtained from most structural analysis software packages, it can be shown that running an algorithm considering material nonlinearity by itself will produce reasonably accurate results. Moreover, separately running an algorithm considering geometric nonlinearity also can produce accurate results. However, when material nonlinearity is combined with geometric nonlinearity in an analysis, obtaining accurate results or even stable solutions is more difficult. The coupling effect between the two nonlinearities can significantly affect the global response and the local plastic rotation obtained from the analysis and therefore needs to be verified through some analytical means. Yet, the verification process is difficult because a robust analytical framework for calculating plastic rotation is currently unavailable and urgently needed. In view of this gap, an improved analytical approach based on small displacement theory is derived to calculate the plastic rotations of plastic hinges at various locations of moment-resisting frames. Both static and dynamic analysis with nonlinear geometric effects will be incorporated in the derivation. Here the element stiffness matrices are first rigorously derived using a member with plastic hinges in compression, and therefore the coupling of geometric and material nonlinearity effects is included from the beginning of the derivation. Additionally, plastic rotation is handled explicitly by considering this rotation as an additional nonlinear degree-of-freedom. Numerical simulation is performed to calculate the nonlinear static and dynamic responses of simple benchmark models subjected to seismic excitations. Results are compared with various software packages to demonstrate the feasibility of the proposed method in light of the output results among software packages in calculating plastic rotations.

This research investigates numerically the potential failure of different framed structures after removal of a corner column. This study is directed towards the role of the joint above the removed column in terms of framed structures stability and internal forces redistribution utilizing linear static, nonlinear static and nonlinear dynamic analysis procedures. First, the preliminary linear static analysis as a part of more detailed nonlinear static and dynamic analysis to model reinforced concrete frames is performed. For nonlinear numerical models, three different moment-rotation capacity curves are considered for the joint above the removed column. These curves are taken according to FEMA 356 regulation according to the reinforcement condition at the joint location to represent normal joint, anchorage deficient joint and shear deficient joint. In linear static models, the results confirmed that, the more moment the joint can resist at the removed column location, the less moment is generated at the beam’s other end. In nonlinear static analysis, the model with normal plastic hinge properties recorded a higher carrying capacity than the model with both shear and anchorage plastic hinges. Nonlinear dynamic analysis with less assumptions offer the more representative modeling for the considered case study which is obvious from its closer perdition of internal forces and deflection compared to the reference findings.

BackgroundConsidering that brain activity involves communication between millions of neurons in a complex network, nonlinear analysis is a viable tool for studying electroencephalography (EEG). The main objective of this review was to collate studies that utilized chaotic measures and nonlinear dynamical analysis in EEG of multiple sclerosis (MS) patients and to discuss the contributions of chaos theory techniques to understanding, diagnosing, and treating MS.MethodsUsing the preferred reporting items for systematic reviews and meta-analysis (PRISMA), the databases EbscoHost, IEEE, ProQuest, PubMed, Science Direct, Web of Science, and Google Scholar were searched for publications that applied chaos theory in EEG analysis of MS patients.ResultsA bibliographic analysis was performed using VOSviewer software keyword co-occurrence analysis indicated that MS was the focus of the research and that research on MS diagnosis has shifted from conventional methods, such as magnetic resonance imaging, to EEG techniques in recent years. A total of 17 studies were included in this review. Among the included articles, nine studies examined resting-state, and eight examined task-based conditions.ConclusionAlthough nonlinear EEG analysis of MS is a relatively novel area of research, the findings have been demonstrated to be informative and effective. The most frequently used nonlinear dynamics analyses were fractal dimension, recurrence quantification analysis, mutual information, and coherence. Each analysis selected provided a unique assessment to fulfill the objective of this review. While considering the limitations discussed, there is a promising path forward using nonlinear analyses with MS data.

While significant advances have been made on the blast analysis, applications of nonlinear analysis of structures under explosion have been limited to the frames and structural behavior of bridges subjected to blast is an issue that has attracted attention of researchers in recent years. Nonlinear dynamic analysis can be lead to the most accurate responses of the structure under blast but the use of it is not justified in many cases because of its complexity and excessive computing times. Pushover method is often seen to be a viable and attractive alternative to nonlinear analysis because of its simplicity and ability to estimate deformation demands with acceptable accuracy without the intensive computational and modeling effort of a nonlinear dynamic analysis. In this study, a rectangular load pattern is developed to estimate nonlinear responses of composite bridges subjected to blast using pushover method. For this purpose, first, an efficient method is proposed to determine equivalent static blast loading and then the accuracy of pushover analysis based on the developed load pattern is evaluated. It is shown that the proposed method can be easily used to conservatively estimate maximum displacement of composite steel girder bridges under explosion.

Non-linear seismic response of concrete gravity dams to near-fault ground motions including dam-water-sediment-foundation interaction