Buckling Thresholds for Pre-Loaded Spherical Shells Subject to Localized Blasts

2019 ◽  
Vol 87 (3) ◽  
Author(s):  
Jan Sieber ◽  
John W. Hutchinson ◽  
J. Michael T. Thompson
Keyword(s):  
Impact Energy ◽  
Energy Barrier ◽  
Threshold Energy ◽  
External Pressure ◽  
Extensive Study ◽  
Energy Threshold ◽  
Integration Scheme ◽  
Spherical Shells ◽  
Buckling Mode ◽  
The Impact

Abstract This paper investigates the robustness against localized impacts of elastic spherical shells pre-loaded under uniform external pressure. We subjected a pre-loaded spherical shell that is clamped at its equator to axisymmetric blast-like impacts applied to its polar region. The resulting axisymmetric dynamic response is computed for increasing amplitudes of the blast. Both perfect shells and shells with axisymmetric geometric imperfections are analyzed. The impact energy threshold causing buckling is identified and compared with the energy barrier that exists between the buckled and unbuckled static equilibrium states of the energy landscape associated with the pre-loaded pressure. The extent to which the impact energy of the threshold blast exceeds the energy barrier depends on the details of its shape and width. Targeted blasts that approximately replicate the size and shape of the energy barrier buckling mode defined in the paper have an energy threshold that is only modestly larger than the energy barrier. An extensive study is carried out for more realistic Gaussian-shaped blasts revealing that the buckling threshold energy for these blasts is typically in the range of at least 10–40% above the energy barrier, depending on the pressure pre-load and the blast width. The energy discrepancy between the buckling threshold and energy barrier is due to elastic waves spreading outward from the impact and dissipation associated with the numerical integration scheme. Buckling is confined to the vicinity of the pole such that, if the shell is not shallow, the buckling thresholds are not strongly dependent on the location of the clamping boundary, as illustrated for a shell clamped halfway between the pole and the equator.

scholarly journals Nonlinear dynamics of spherical shells buckling under step pressure

2019 ◽  
Vol 475 (2223) ◽  
pp. 20180884 ◽  
Author(s):  
Jan Sieber ◽  
John W. Hutchinson ◽  
J. Michael T. Thompson
Keyword(s):  
Nonlinear Dynamics ◽  
External Pressure ◽  
Dynamic Buckling ◽  
Spherically Symmetric ◽  
Imperfection Sensitivity ◽  
Spherical Shells ◽  
Buckling Mode ◽  
Geometric Imperfections ◽  
Pressure Threshold ◽  
Initial Geometric Imperfections

Dynamic buckling is addressed for complete elastic spherical shells subject to a rapidly applied step in external pressure. Insights from the perspective of nonlinear dynamics reveal essential mathematical features of the buckling phenomena. To capture the strong buckling imperfection-sensitivity, initial geometric imperfections in the form of an axisymmetric dimple at each pole are introduced. Dynamic buckling under the step pressure is related to the quasi-static buckling pressure. Both loadings produce catastrophic collapse of the shell for conditions in which the pressure is prescribed. Damping plays an important role in dynamic buckling because of the time-dependent nonlinear interaction among modes, particularly the interaction between the spherically symmetric ‘breathing’ mode and the buckling mode. In general, there is not a unique step pressure threshold separating responses associated with buckling from those that do not buckle. Instead, there exists a cascade of buckling thresholds, dependent on the damping and level of imperfection, separating pressures for which buckling occurs from those for which it does not occur. For shells with small and moderately small imperfections, the dynamic step buckling pressure can be substantially below the quasi-static buckling pressure.

Buckling Analyses of Spherical Shells by the Finite Element Method Based on the Willis-Form Equations

2019 ◽  
Vol 11 (09) ◽  
pp. 1950091 ◽  
Author(s):  
Yixiao Sun ◽  
Zhihai Xiang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
External Pressure ◽  
Experimental Results ◽  
Spherical Shells ◽  
Buckling Loads ◽  
Geometrical Imperfections ◽  
The Impact ◽  
Previous Loading ◽  
Element Method

Buckling analysis of spherical shells under external pressure is a crucial problem in mechanical and aerospace engineering. It is widely known that the buckling loads obtained by classical methods are much higher than experimental results. The main reason for this large discrepancy is customarily attributed to initial geometrical imperfections, and the impact of inhomogeneously distributed stresses during loading process is usually ignored. In order to investigate the effect of this ignored factor, the buckling loads of several spherical shells are analyzed by the geometrically nonlinear finite element method (FEM) based on the Willis-form equations, which explicitly contain the stress gradients at previous loading step. It can be shown that the buckling loads from the Willis-form FEM are about 10% lower than the values from classical FEM. This finding may give better understandings to the differences between theoretical and experimental results for nearly perfect spherical shells and may be helpful to obtain more accurate buckling loads for shells with initial geometrical imperfections.

scholarly journals Nonlinear buckling behaviour of spherical shells: barriers and symmetry-breaking dimples

2017 ◽  
Vol 375 (2093) ◽  
pp. 20160154 ◽  
Author(s):  
John W. Hutchinson ◽  
J. Michael T. Thompson
Keyword(s):  
Symmetry Breaking ◽  
Large Range ◽  
External Pressure ◽  
Media Theory ◽  
Spherical Shells ◽  
Buckling Mode ◽  
Nonlinear Buckling ◽  
Accurate Evaluation ◽  
Post Buckling ◽  
Volume Controlled

The nonlinear axisymmetric post-buckling behaviour of perfect, thin, elastic spherical shells subject to external pressure and their asymmetric bifurcations are characterized, providing results for a structure/loading combination with an exceptionally nonlinear buckling response. Immediately after the onset of buckling, the buckling mode localizes into a dimple at the poles. The relations among the pressure, the dimple amplitude and the change in volume of the shell are determined over a large range of pole deflections. These results allow accurate evaluation of criteria such as the Maxwell condition for which the energies in the unbuckled and buckled states are the same and evaluation of the influences of pressure versus volume-controlled loadings. Non-axisymmetric bifurcation from the axisymmetric state, which occurs deep into the post-buckling regime in the form of multi-lobed dimples, is also established and discussed. This article is part of the themed issue ‘Patterning through instabilities in complex media: theory and applications.’

Nonlinear Buckling Interaction for Spherical Shells Subject to Pressure and Probing Forces

2017 ◽  
Vol 84 (6) ◽  
Author(s):  
John W. Hutchinson ◽  
J. Michael T. Thompson
Keyword(s):  
Internal Pressure ◽  
Energy Barrier ◽  
Constant Pressure ◽  
External Pressure ◽  
Constant Volume ◽  
Uniform Pressure ◽  
Loading Conditions ◽  
Spherical Shells ◽  
Nonlinear Buckling ◽  
Axisymmetric State

Elastic spherical shells loaded under uniform pressure are subject to equal and opposite compressive probing forces at their poles to trigger and explore buckling. When the shells support external pressure, buckling is usually axisymmetric; the maximum probing force and the energy barrier the probe must overcome are determined. Applications of the probing forces under two different loading conditions, constant pressure or constant volume, are qualitatively different from one another and fully characterized. The effects of probe forces on both perfect shells and shells with axisymmetric dimple imperfections are studied. When the shells are subject to internal pressure, buckling occurs as a nonaxisymmetric bifurcation from the axisymmetric state in the shape of a mode with multiple circumferential waves concentrated in the vicinity of the probe. Exciting new experiments by others are briefly described.

Response and failure modes of biaxial warp-knitted flexible composite subject to low-velocity impact

2021 ◽  
pp. 152808372110154
Author(s):  
Ziyu Zhao ◽  
Tianming Liu ◽  
Pibo Ma
Keyword(s):  
Impact Energy ◽  
Linear Density ◽  
Failure Modes ◽  
Impact Response ◽  
Low Velocity Impact ◽  
Minor Effect ◽  
Low Velocity ◽  
Velocity Impact ◽  
Flexible Composites ◽  
The Impact

In this paper, biaxial warp-knitted fabrics were produced with different high tenacity polyester linear density and inserted yarns density. The low-velocity impact property of flexible composites made of polyurethane as matrix and biaxial warp-knitted fabric as reinforcement has been investigated. The effect of impactor shape and initial impact energy on the impact response of flexible composite is tested. The results show that the initial impact energy have minor effect on the impact response of the biaxial warp-knitted flexible composites. The impact resistance of flexible composite specimen increases with the increase of high tenacity polyester linear density and inserted yarns density. The damage morphology of flexible composite materials is completely different under different impactor shapes. The findings have theoretical and practical significance for the applications of biaxial warp-knitted flexible composite.

scholarly journals Impact resistance of steel materials to ballistic ejecta and shelter development using steel deck plates

2021 ◽  
Vol 10 (1) ◽  
Author(s):  
Hiroyuki Yamada ◽  
Kohei Tateyama ◽  
Shino Naruke ◽  
Hisashi Sasaki ◽  
Shinichi Torigata ◽  
...  
Keyword(s):  
Impact Energy ◽  
Impact Test ◽  
Impact Resistance ◽  
Protective Layer ◽  
High Strength ◽  
Steel Plates ◽  
Corrugated Plates ◽  
Shelter Construction ◽  
The Impact ◽  
Ballistic Ejecta

AbstractThe destruction caused by ballistic ejecta from the phreatic eruptions of Mt. Ontake in 2014 and Mt. Kusatsu-Shirane (Mt. Moto-Shirane) in 2018 in Japan, which resulted in numerous casualties, highlighted the need for better evacuation facilities. In response, some mountain huts were reinforced with aramid fabric to convert them into shelters. However, a number of decisions must be made when working to increase the number of shelters, which depend on the location where they are to be built. In this study, we propose a method of using high-strength steel to reinforce wooden buildings for use as shelters. More specifically, assuming that ballistic ejecta has an impact energy of 9 kJ or more, as in previous studies, we developed a method that utilizes SUS304 and SS400 unprocessed steel plates based on existing impact test data. We found that SUS304 is particularly suitable for use as a reinforcing material because it has excellent impact energy absorption characteristics due to its high ductility as well as excellent corrosion resistance. With the aim of increasing the structural strength of steel shelters, we also conducted an impact test on a shelter fabricated from SS400 deck plates (i.e., steel with improved flexural strength provided by work-hardened trapezoidal corrugated plates). The results show that the shelter could withstand impact with an energy of 13.5 kJ (2.66 kg of simulated ballistic ejecta at 101 m/s on impact). In addition, from the result of the impact test using the roof-simulating structure, it was confirmed the impact absorption energy is further increased when artificial pumice as an additional protective layer is installed on this structure. Observations of the shelter after the impact test show that there is still some allowance for deformation caused by projectile impact, which means that the proposed steel shelter holds promise, not only structurally, but also from the aspects of transportation and assembly. Hence, the usefulness of shelters that use steel was shown experimentally. However, shelter construction should be suitable for the target environment.

Geometrically nonlinear static and dynamic analysis of CNT reinforced laminated composite plates: A finite element study

2021 ◽  
pp. 095440622110089
Author(s):  
Balakrishna Adhikari ◽  
BN Singh
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Dynamic Response ◽  
Integration Scheme ◽  
Static And Dynamic Analysis ◽  
Finite Element Study ◽  
Nonlinear Eigenvalues ◽  
Nonlinear Static ◽  
The Impact ◽  
Element Study

In this paper, a finite element study is conducted using the Green Lagrange strain field based on vonKarman assumptions for the geometric nonlinear static and dynamic response of the laminated functionally graded CNT reinforced (FG-CNTRC) composite plate. The governing equations for determining the nonlinear static and dynamic behavior of the FG-CNTRC plate are derived using the Lagrange equation of motion based on Reddy's higher order theory. Using the direct iteration technique, the nonlinear eigenvalues for analyzing the free vibration response are obtained and the nonlinear dynamic responses of the FG-CNTRC plate are encapsulated based on the nonlinear Newmark integration scheme. The impact of the amplitude of vibration on mode switching phenomena and the consequence of the duration of the pulse on the free vibration regime of the plate are outlined. Also, the effect of time dependent loads is studied on the normal stresses of the plate. Furthermore, the impact on the nonlinear static and dynamic response of the laminated FG-CNTRC plate of various parameters such as span-thickness ratio (b/h ratio), aspect ratio (a/b ratio), different edge constraints, CNT fiber gradation, etc. are also studied.

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