Нелинейная устойчивость синусоидальной велароидальной оболочки

State-of-the-art nonlinear computational analysis of shells, nonlinearities due to large deformations and nonlinear material behavior, alternative shell element formulations, algorithms and implementational aspects, composite and sandwich shells, local and global instabilities, optimization of shell structures and concepts of shape finding methods of free from shells. Furthermore, algorithms for the treatment of the nonlinear stability behavior of shell structures (including bifurcation and snap-through buckling) are presented in the book.

A local–global FE model for nonlinear analysis of column-supported shells of revolution

Finite- and boundary-element linear and nonlinear analyses of shells and shell-like structures: A bibliography (1999–2001)

Procedures are investigated by which nonlinear finite element shell analysis algorithms can be simplified to provide more cost effective approximate analyses of orthogonally-reinforced concrete flat plate structures. Two alternative effective stiffness formulations, and an unbalanced force formulation, are described. These are then implemented into a nonlinear shell analysis algorithm. Nonlinear geometry, three-dimensional layered stress analyses, and other general formulations are bypassed to reduce the computational burden. In application to standard patch test problems, these simplified approximate analysis procedures are shown to provide reasonable accuracy while significantly reducing the computational effort. Corroboration studies using various simple and complex test specimens provide an indication of the relative accuracy of the constitutive models utilized. The studies also point to the limitations of the approximate formulations, and identify situations where one should revert back to full nonlinear shell analyses.

A refined non-conforming triangular plate/shell element for linear and geometrically nonlinear analysis of plates and shells is developed in this paper based on the refined non-conforming element method (RNEM). A conforming triangle membrane element with drilling degrees of freedom in Cartesian coordinates and the refined non-conforming triangular plate-bending element RT9, in which Kirchhoff kinematic assumption was adopted, are used to construct the present element. The displacement continuity condition along the interelement boundary is satisfied in an average sense for plate analysis, and the coupled displacement continuity requirement at the interelement is satisfied in an average sense, thereby improving the performance of the element for shell analysis. Selectively reduced integration with stabilization scheme is employed in this paper to avoid membrane locking. Numerical examples demonstrate that the present element behaves quite satisfactorily either for the linear analysis of plate bending problems and plane problems or for the geometrically nonlinear analysis of thin plates and shells with large displacement, moderate rotation but small strain.

Geometrically non-linear analysis of arbitrary elastic supported plates and shells using an element-based Lagrangian shell element

Nonlinear analysis of FG-sandwich plates and shells

Nonlinear large deformation analysis of shells using the variational differential quadrature method based on the six-parameter shell theory

Sensitivity analysis and shape optimization in nonlinear solid mechanics

Beam-like, architected microstructures (BAMs) can be used in various functional applications, such as micro-electro-mechanical systems (MEMS), energy harvesting, actuation, etc. Designing with high aspect ratios under large deformations, BAMs typically experience severe buckling instability. Therefore, it is of necessity to investigate the mechanical behaviors with respect to the geometric and material nonlinearities. This paper proposes a bilinear size-dependent model using the modified couple stress theory to full formulate the buckling response of the BAMs. Buckling-induced large deformation is studied using the geometric nonlinearity, and the recoverability is investigated based on the material nonlinearity. Experiments and numerical simulations are conducted to validate the theoretical results at the macroscale and microscale, respectively, and satisfactory agreements are obtained. Parametric studies are carried out to study the effects of the material length scale factor-to-thickness ratio χ=lt (i.e., geometric nonlinearity) and plastic factor η (i.e., material nonlinearity). χ and η are further discussed with respect to the effective bending stiffness B¯PAM and volume V¯PAM of the microstructures. The theoretical model presented in this study can be used to predict and tune the mechanical response of BAMs with different architected webbing patterns.

Postbuckling performance of the TRIC natural mode triangular element for Isotropic and laminated composite shells

Many numerical methods of analysis of rigid shells, such as the displacement-based finite element method (FEM), finite difference energy method, method of separation of variables, kinematic method of the theory of limit equilibrium, and so on, were proposed and tested until 2000. Most problems of static and dynamic analysis of canonical shells were successfully solved at the same time. All these methods were used actively after the 2000, too. However, new problems began to appear before structural engineers, architects, and builders. These problems are associated with multi-layer shell walls, with the emergence of new composite construction materials, and therefore, with the solution of physically nonlinear problems. Geometricians presented several hundred new forms of middle surfaces of shells, and that is why the need to select optimal forms from several alternatives using criteria of optimality came into existence. The selection of necessary computing software from many of their types began to be a problem. New problems demanded new methods of approach for their solution. In this paper, a critical evaluation of proposed solutions on strength, stability, and vibration analysis of shells was conducted in connection with new problems that appeared after the year 2000. Rigid shells in the form of analytical surfaces, designed using the canon of parametric architecture, were taken as an example. Analytical middle surfaces of shells, which attracted the attention of architects after 2000, are pointed out, and suitable methods of analysis of these shells are noted for the first time. The review was compiled based on 112 fundamental scientific works published after 2000. Other scientific reviews devoted to the investigation of joint problems of geometry, application, and calculation of assembled rigid thin-walled shells with analytical middle surfaces were not found.

Geometrically nonlinear analysis of laminate composite plates and shells using the eight-node hexahedral element with one-point integration

This paper presents a computationally efficient numerical model for the analysis of thin shells based on rotation-free triangular finite elements. The geometry of the structure in the vicinity of the observed triangular element is approximated through a controlled domain consisting of nodes of the observed finite element and nodes of three adjacent finite elements between which a second-order spatial polynomial is defined. The model considers large displacements, large rotations, small strains, and material and geometrical nonlinearity. Material nonlinearity is implemented by considering the von Mises yield criterion and the Levi–Mises flow rule. The model uses an explicit time integration scheme to integrate motion equations but an implicit radial returning algorithm to compute the plastic strain at the end of each time step. The presented numerical model has been embedded in the program Y based on the finite–discrete element method and tested on simple examples. The advantage of the presented numerical model is displayed through a series of analyses where the obtained results are compared with other results presented in the literature.

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.