Optimal Forms of Shallow Shells With Circular Boundary, Part 2: Maximum Buckling Load

1984 ◽  
Vol 51 (3) ◽  
pp. 531-535 ◽  
Author(s):  
R. H. Plaut ◽  
L. W. Johnson
Keyword(s):  
Critical Load ◽  
Elastic Shell ◽  
Material Surface ◽  
Fundamental Vibration ◽  
Uniform Loading ◽  
Concentrated Load ◽  
Shallow Shells ◽  
Simply Supported ◽  
Circular Boundary ◽  
Boundary Part

In Part 1, optimal forms were determined for maximizing the fundamental vibration frequency of a thin, shallow, axisymmetric, elastic shell with given circular boundary. Our objective in this part is to maximize the critical load for buckling under a uniformly distributed load or a concentrated load at the center. Again, the shell form is varied and the material, surface area, and uniform thickness of the shell are specified. Both clamped and simply supported boundary conditions are considered for the case of uniform loading, while one example is presented involving a concentrated load acting on a clamped shell. The optimality condition leads to forms that have zero slope at the boundary if it is clamped. The maximum critical load is sometimes associated with a limit point and sometimes with a bifurcation point. It is often substantially higher than the critical load for the corresponding spherical shell.

Optimal Forms of Shallow Shells With Circular Boundary, Part 3: Maximum Enclosed Volume

1984 ◽  
Vol 51 (3) ◽  
pp. 536-539 ◽  
Author(s):  
R. H. Plaut ◽  
L. W. Johnson
Keyword(s):  
Spherical Shell ◽  
Surface Area ◽  
Material Surface ◽  
Uniform Thickness ◽  
Base Plane ◽  
Shallow Shells ◽  
Simply Supported ◽  
Circular Boundary ◽  
Boundary Part ◽  
Uniformly Distributed Loads

In Parts 1 and 2, we determined optimal forms of shallow shells with respect to vibration and stability, respectively. In this final part, we consider a given load and find the shell form for which the volume between the base plane and the deflected shell is a maximum. As before, the shell is assumed to be thin, elastic, and axisymmetric, with a given circular boundary that is either clamped or simply supported. The material, surface area, and uniform thickness of the shell are specified. Both uniformly distributed loads and concentrated central loads are treated. In the numerical results, the maximum enclosed volume is on the order of 10 percent higher than that for the corresponding spherical shell.

Optimal Forms of Shallow Shells With Circular Boundary, Part 1: Maximum Fundamental Frequency

1984 ◽  
Vol 51 (3) ◽  
pp. 526-530 ◽  
Author(s):  
R. H. Plaut ◽  
L. W. Johnson ◽  
R. Parbery
Keyword(s):  
Boundary Conditions ◽  
Fundamental Frequency ◽  
Iterative Procedure ◽  
Material Surface ◽  
Uniform Thickness ◽  
Shallow Shells ◽  
Simply Supported ◽  
Circular Boundary ◽  
Axisymmetric Shell ◽  
Boundary Part

Thin, shallow, elastic shells with given circular boundary are considered. We seek the axisymmetric shell form which maximizes the fundamental frequency of vibration. The boundary conditions, material, surface area, and uniform thickness of the shell are specified. We employ a bimodal formulation and use an iterative procedure based on the optimality condition to obtain optimal forms. Results are presented for clamped and simply supported boundary conditions. For the clamped case, the optimal forms have zero slope at the boundary. The maximum fundamental frequency is significantly higher than that for the corresponding spherical shell if the boundary is clamped, but only slightly higher if it is simply supported.

Propagation of Axisymmetric Waves in an Unlimited Elastic Shell

1960 ◽  
Vol 27 (4) ◽  
pp. 690-695 ◽  
Author(s):  
A. Kalnins ◽  
P. M. Naghdi
Keyword(s):  
Spherical Shell ◽  
Entire Range ◽  
Energy Input ◽  
Elastic Shell ◽  
Mechanical Impedance ◽  
Stress Waves ◽  
Axisymmetric Stress ◽  
Spherical Shells ◽  
Concentrated Load ◽  
Shallow Shells

This investigation is concerned with the propagation of axisymmetric stress waves in unlimited thin shallow elastic spherical shells. In particular, a solution is obtained for an unlimited shallow spherical shell subjected to a harmonically oscillating concentrated load at the apex. This solution, exact within the scope of the linear theory of shallow shells, has an outward propagating wave character in the entire range of forcing frequency. Appropriate expressions for the mechanical impedance and the energy input are derived, and numerical results are obtained for the axial displacement corresponding to various forcing frequencies.

The Significance of the Concentrated Load in the Limit Analysis of Conical Shells

1966 ◽  
Vol 33 (1) ◽  
pp. 93-101 ◽  
Author(s):  
John A. DeRuntz ◽  
P. G. Hodge
Keyword(s):  
Yield Condition ◽  
Point Load ◽  
Concentrated Load ◽  
Shallow Shells ◽  
Conical Shells ◽  
Simply Supported ◽  
Tresca Yield Condition ◽  
Wide Range ◽  
Limiting Case ◽  
Yield Conditions

The yield point load of a simply supported conical sandwich shell loaded at its vertex through a rigid central boss is found for a material obeying the Tresca yield condition. Exact solutions are found for a wide range of shell configurations ranging from thick shallow cones to thin steep ones, including large and small boss sizes. The results are compared with those for the limiting case of zero boss radius corresponding to a complete conical shell loaded with a concentrated load at its vertex. It is found that for thick shallow shells the concentrated-load solution is a good approximation to the solution for realistically small boss sizes, but that for thin and/or steep shells the agreement is so poor as to make the concentrated-load solution meaningless. It is shown that such behavior also can be expected for shells obeying more realistic yield conditions.

Local loads on a toroidal shell

1992 ◽  
Vol 27 (2) ◽  
pp. 59-66 ◽  
Author(s):  
D Redekop ◽  
F Zhang
Keyword(s):  
Cylindrical Shell ◽  
Shell Theory ◽  
Elastic Shell ◽  
Toroidal Shell ◽  
Pipe Bend ◽  
Local Loads ◽  
Simply Supported ◽  
Linear Elastic ◽  
Wide Range ◽  
Theory Solution

In this study the effect of local loads applied on a sectorial toroidal shell (pipe bend) is considered. A linear elastic shell theory solution for local loads is first outlined. The solution corresponds to the case of a shell simply supported at the two ends. Detailed displacement and stress results are then given for a specific shell with loadings centred at three positions; the crown circles, the extrados, and the intrados. These results are compared with results for a corresponding cylindrical shell. The paper concludes with a table summarizing results for characteristic displacements and stresses in a number of shells, covering a wide range of geometric parameters.

Dynamic Instability Analysis and Design Charts of Curved Panels with Linearly Varying Periodic In-Plane Load

2021 ◽  
pp. 2150130
Author(s):  
G. Patel ◽  
A. N. Nayak ◽  
A. K. L. Srivastava
Keyword(s):  
Finite Element ◽  
Boundary Conditions ◽  
Dynamic Instability ◽  
Excitation Frequency ◽  
Instability Region ◽  
Concentrated Load ◽  
Simply Supported ◽  
Finite Element Software ◽  
Design Charts ◽  
Curved Panels

The present paper reports an extensive study on dynamic instability characteristics of curved panels under linearly varying in-plane periodic loading employing finite element formulation with a quadratic isoparametric eight nodded element. At first, the influences of three types of linearly varying in-plane periodic edge loads (triangular, trapezoidal and uniform loads), three types of curved panels (cylindrical, spherical and hyperbolic) and six boundary conditions on excitation frequency and instability region are investigated. Further, the effects of varied parameters, such as shallowness parameter, span to thickness ratio, aspect ratio, and Poisson’s ratio, on the dynamic instability characteristics of curved panels with clamped–clamped–clamped–clamped (CCCC) and simply supported-free-simply supported-free (SFSF) boundary conditions under triangular load are studied. It is found that the above parameters influence significantly on the excitation frequency, at which the dynamic instability initiates, and the width of dynamic instability region (DIR). In addition, a comparative study is also made to find the influences of the various in-plane periodic loads, such as uniform, triangular, parabolic, patch and concentrated load, on the dynamic instability behavior of cylindrical, spherical and hyperbolic panels. Finally, typical design charts showing DIRs in non-dimensional forms are also developed to obtain the excitation frequency and instability region of various frequently used isotropic clamped spherical panels of any dimension, any type of linearly varying in-plane load and any isotropic material directly from these charts without the use of any commercially available finite element software or any developed complex model.

scholarly journals Dynamic Stability Critical State of Pin-Ended Arches under Sudden Central Concentrated Load

Mechanika ◽  
2020 ◽  
Vol 26 (5) ◽  
Author(s):  
Kai QIN ◽  
Jingyuan LI ◽  
Mengsha LIU ◽  
Jinsan JU
Keyword(s):  
Finite Element ◽  
Critical Load ◽  
Critical State ◽  
Elastic Strain ◽  
Strain Energy ◽  
Elastic Strain Energy ◽  
The State ◽  
Energy Principle ◽  
Concentrated Load ◽  
Elastic Plastic

The dynamic in-plane instability process of extreme point type for pin-ended arches when a central radial load applied suddenly with infinite duration is analyzed with finite element method in this study. The state of arch can be determined by the crown’s vertical displacement varied with time and the critical load can be obtained by repeating trial-calculation. When the arch structure reaches the dynamically stable critical state, the kinetic energy of the structure is very small or even zero. The dynamic critical load of elastic arch calculated with the theoretical analysis method which is based on energy principle is proved accuracy enough by comparing with the finite element calculation results and the percentage of the differences between them are no more than 4.5 %. The maximal elastic strain energy is certain for the elastic-plastic arch in certain geometry under both a sudden load and static load. The maximal elastic strain energy in static calculation can be used in determining the state of the elastic-plastic arch under dynamic sudden loads applied and this method is more accurate which errors won’t exceed 3.5 %. The accuracy of dynamic critical load calculation method for elastic arch is verified by numerical calculation in this study, and based on the characteristic of elastic strain energy in critical state, a method for determining the stability of elastic-plastic arch is presented.

Performance of Reinforced Concrete Beams with Multiple Openings

2020 ◽  
Vol 857 ◽  
pp. 162-168
Author(s):  
Haidar Abdul Wahid Khalaf ◽  
Amer Farouk Izzet
Keyword(s):  
Reinforced Concrete ◽  
Ultimate Load ◽  
Concrete Beams ◽  
Load Capacity ◽  
Reinforced Concrete Beams ◽  
Design Parameters ◽  
Ultimate Load Capacity ◽  
Concentrated Load ◽  
Simply Supported ◽  
Group I

The present investigation focuses on the response of simply supported reinforced concrete rectangular-section beams with multiple openings of different sizes, numbers, and geometrical configurations. The advantages of the reinforcement concrete beams with multiple opening are mainly, practical benefit including decreasing the floor heights due to passage of the utilities through the beam rather than the passage beneath it, and constructional benefit that includes the reduction of the self-weight of structure resulting due to the reduction of the dead load that achieves economic design. To optimize beam self-weight with its ultimate resistance capacity, ten reinforced concrete beams having a length, width, and depth of 2700, 100, and 400 mm, respectively were fabricated and tested as simply supported beams under one incremental concentrated load at mid-span until failure. The design parameters were the configuration and size of openings. Three main groups categorized experimental beams comprise the same area of openings and steel reinforcement details but differ in configurations. Three different shapes of openings were considered, mainly, rectangular, parallelogram, and circular. The experimental results indicate that, the beams with circular openings more efficient than the other configurations in ultimate load capacity and beams stiffness whereas, the beams with parallelogram openings were better than the beams with rectangular openings. Commonly, it was observed that the reduction in ultimate load capacity, for beams of group I, II, and III compared to the reference solid beam ranged between (75 to 93%), (65 to 93%), and (70 to 79%) respectively.

scholarly journals Peridynamic Higher-Order Beam Formulation

2020 ◽  
Author(s):  
Zhenghao Yang ◽  
Erkan Oterkus ◽  
Selda Oterkus
Keyword(s):  
Finite Element Method ◽  
Cantilever Beam ◽  
Higher Order ◽  
Point Load ◽  
Transverse Displacement ◽  
Lagrange Equations ◽  
Concentrated Load ◽  
Simply Supported Beam ◽  
Simply Supported ◽  
Good Agreement

Abstract In this study, a novel higher-order peridynamic beam formulation is presented. The formulation is obtained by using Euler-Lagrange equations and Taylor’s expansion. To demonstrate the capability of the presented approach, several different beam configurations are considered including simply supported beam subjected to distributed loading, simply supported beam with concentrated load, clamped-clamped beam subjected to distributed loading, cantilever beam subjected to a point load at its free end and cantilever beam subjected to a moment at its free end. Transverse displacement results along the beam obtained from peridynamics and finite element method are compared with each other and very good agreement is obtained between the two approaches.

scholarly journals Analysis of simply supported wood beams at ambient and high temperatures

2018 ◽  
Vol 7 (2.23) ◽  
pp. 180 ◽  
Author(s):  
Elza M M Fonseca ◽  
Pedro J V Gouveia
Keyword(s):  
High Temperatures ◽  
Cross Sections ◽  
Beam Theory ◽  
Sufficient Accuracy ◽  
Load Bearing Capacity ◽  
Concentrated Load ◽  
Standard Methods ◽  
Simply Supported ◽  
Wood Beams ◽  
Safe Load

The main objective of this work is to present a methodology for safety analysis of simply supported wood beams at ambient and high temperatures with a concentrated load at mid-span. Sixteen different beam configurations will be studied. All calculations were conducted according the Eurocode 5, part 1-1 and part 1-2. During this study will be analyzed the safe load bearing capacity according standards and compared with the elastic and plastic load from beam theory. The beam theory can provide sufficient accuracy up to the point of instability. The standard methods are generally conservative and they are suitable to be used for design purposes with safety. The studied beam cross sections will be in glued laminated wood, as yellow birch, with characteristics equals to a Glulam GL28H. 

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