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Cantilever column critical dynamic instability load under nonconservative follower force including thermomechanical coupling effect from boundary value problem formulation
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A three m diameter by three m long corrugated cylindrical shell with external stiffening rings was tested to failure by buckling. The corrugation geometry for the graphite epoxy composite cylinder wall was optimized to withstand a compressive load producing an ultimate load intensity of 157.6 kN/m without buckling. The test method used to produce the design load intensity was to mount the specimen as a cantilevered cylinder and apply a pure bending moment to the end. A load introduction problem with the specimen was solved by using the BOSOR 4 shell of revolution computer code to analyze the shell and attached loading fixtures. The cylinder test loading achieved was 101 percent of design ultimate, and the resulting mass per unit of shell wall area was 1.96 kg/sq m.
The problem of an orthotropic cantilevered plate subjected to a uniformly distributed end load is solved by the Rayleigh-Ritz energy method. The result is applied to laminated composite, double cantilevered specimens to estimate the effect of crack tip constraint on the transverse curvature, deflection and energy release rate. The solution is also utilized to determined finite width correction factors for fracture energy characterization tests in which neither plane stress nor plane strain conditions apply.
Cantilevered column stability under constant follower load in presence of external damping
An experimental investigation was conducted at the Langley aircraft landing loads and traction facility to define the cornering characteristics of a size C40 x14-21 aircraft tire of cantilever design. These characteristics, which include the cornering-force and drag-force friction coefficients and self-alining torque, were obtained for the tire operating on dry, damp, and flooded runway surfaces over a range of yaw angles from 0 deg to 20 deg and at ground speeds of 5 to 100 knots, both with and without braking. The results of this investigation show that the cornering-force and drag-force friction coefficients and self-alining torque were influenced by the yaw angle, ground speed, brake torque, surface wetness, and the locked-wheel condition.
Tubes apply as displacement is registered by long armed, double-cantilever gage. Sharp points at ends of arms protrude through holes in tube walls and contact center of area of load applications. Method was devised for determining load point displacement accurately. No extraneous displacement fraction is present in measurement, and data-correction procedures are unnecessary.
The Shock and Vibration team within the Test Engineering group at Los Alamos National Laboratory (LANL) aids in the development and qualification of weapon systems for the United States Department of Energy (DOE). Performing tests that replicate shock and vibration environments representative of a weapon’s lifetime is critical in ensuring safety, survivability, and reliability. A key factor in shock and vibration testing is accurate representation of the weapon’s boundary conditions in its end use configuration. The boundary conditions representative of a reentry body in flight are particularly difficult to replicate on an electrodynamic shaker. When executing shock and vibration tests on a reentry body, two system axes are tested with the system in a cantilevered configuration. This cantilevered testing configuration results in a moment load being applied to the system while undergoing vibration environments. A special fixture, known as the Flex-Web, was developed to decouple this moment load from the reentry body in order to more accurately represent real world boundary conditions while replicating flight environments.
The effect of a type of magnetic damping on the stability of equilibrium of some circulatory elastic systems is examined. A simple system with two degrees of freedom is considered first, and a destabilization is found to be caused by the magnetic field. The nature of the destabilization, however, is not identical to that caused by internal viscous damping. The differences and similarities between the two effects are discussed, and the results are also compared with those of linear external viscous damping. A continuous cantilever bar subjected to a follower force at its free end is then examined. It is found that the critical load is independent of the strength of the magnetic field, and is considerably lower than the corresponding critical load in the absence of a magnetic field. Finally, the continuous cantilever is treated approximately by Galerkin's procedure and also by using a two-degree-of-freedom model of the cantilever; the results obtained are qualitatively the same.
Cantilevered structure supports heat exchanger coils against vibration loading while allowing freedom for differential thermal growth. The support channels will accept a variety of coil angles with the same coil pitch, thus reducing the number of parts required. This design, with slight modification, could be used to support parallel rows of straight piping.
An investigation was conducted at the Langley aircraft landing loads and traction facility to determine the cornering characteristics of a 40 x 14-16 type VII aircraft tire. These characteristics, which include the cornering-force and drag-force friction coefficients and self-alining torque, were obtained for the tire operating on dry, damp and flooded runway surfaces over a range of yaw angles from 0 deg to 20 deg and at ground speeds from 5 to 100 knots, both with and without braking. The results of this investigation indicated that the cornering capability of the 40 x 14-16 type VII aircraft tire is degraded by high ground speeds, thin-film lubrication and tire hydroplaning effects on the wet surfaces, and brake torque. The cornering capability is greatly diminished when locked-wheel skids are encountered.
Orion and Commercial Crew Program (CCP) Partners have chosen to use frangible joints for certain separation events. The joints currently available are zero failure tolerant and will be used in mission safety applications. The goal is to further develop a NASA designed redundant frangible joint that will lower flight risk and increase reliability. FY16 testing revealed a successful design in subscale straight test specimens that gained efficiency and supports Orion load requirements. Approach / Innovation A design constraint is that the redundant joint must fit within the current Orion architecture, without the need for additional vehicle modification. This limitation required a design that changed the orientation of the expanding tube assemblies (XTAs), by rotating them 90deg from the standard joint configuration. The change is not trivial and affects the fracture mechanism and structural load paths. To address these changes, the design incorporates cantilevered arms on the break plate. The shock transmission and expansion of the XTA applies force to these arms and creates a prying motion to push the plate walls outward to the point of structural failure at the notched section. The 2014 test design revealed that parts could slip during functioning wasting valuable energy needed to separate the structure with only a single XTA functioning. Dual XTA functioning fully separated the assembly showing a discrepancy can be backed up with redundancy. Work on other fully redundant systems outside NASA is limited to a few patents that have not been subjected to functionality testing Design changes to prevent unwanted slippage (with ICA funding in 2015) showed success with a single XTA. The main goal for FY 2016 was to send the new Flat H RFJ to WSTF where single XTA test failures occurred back in 2014. The plan was to gain efficiency in this design by separating the Flat H RFJ with thicker ligaments with dimensions baselined in 2014. Other modifications included geometry changes to better disperse loads paths and to minimize air gaps. The design additionally added more structural strength to enhance the structural limits in static loads testing. The design also implemented a smoother load line through the assembly. Results / Knowledge Gained The new Flat H RFJ successfully fractured at WSTF with thicker ligaments and lower cord size. Where failure to separate occurred earlier, there is now excessive energy available for structural separation. The new challenge to provide some structural support to prevent secondary fracturing of the break plate remains to be completed. This future work is being funded by the JSC Engineering Directorate in 2017 to elevate the TRL on curved Flat H RFJs that configure with the Orion Service Panel Separation. Additional funding from JSC Engineering will provide new design testing to avoid secondary fracturing.
An indicating device designed to provide an electrical signal relative to the position of a load is described. The device has a central housing with two wing structures on each side which support conventional switch means having cantilevered arms. Extending through the housing is a movable shaft that is spring biased to a forward extended position and adapted to respond against a load being positioned. The rear end of the movable shaft has an adjustable cam means which acts upon the cantilevered ams to cause a switching action upon shifting of the movable shaft by a load.
The paper examines some questions relating to the optimal design of continuous one-dimensional structures driven by harmonically oscillating loads. Optimal-control methods are applied to a cantilever bar driven sinusoidally by an axial force at its tip to illustrate the minimum-weight design of one-dimensional structures under dynamic excitation. Realistic constraints are imposed during the optimizations, including a maximum allowable stress amplitude at any point along the bar and a minimum cross-sectional area. It is shown that in the absence of damping, the design space may contain many disjoint feasible regions, and multiple optima can exist. Detailed solutions are obtained for continuous bars with an excitation frequency less than, and then greater than, the fundamental free-vibration frequency. It is found that above a certain excitation frequency, two or more arcs with different constraints characterize the optimal designs. It is concluded that when more than two different constrained arcs characterize the optimal solution, the continuum approach may be impractical, and finite-element approximations may offer the only alternative.
A three-bay, space, cantilever truss is probabilistically evaluated to describe progressive buckling and truss collapse in view of the numerous uncertainties associated with the structural, material, and load variables that describe the truss. Initially, the truss is deterministically analyzed for member forces, and members in which the axial force exceeds the Euler buckling load are identified. These members are then discretized with several intermediate nodes, and a probabilistic buckling analysis is performed on the truss to obtain its probabilistic buckling loads and the respective mode shapes. Furthermore, sensitivities associated with the uncertainties in the primitive variables are investigated, margin of safety values for the truss are determined, and truss end node displacements are noted. These steps are repeated by sequentially removing buckled members until onset of truss collapse is reached. Results show that this procedure yields an optimum truss configuration for a given loading and for a specified reliability.
An approximation method based on the method of Kantorovich is used to calculate the critical thickness necessary to prevent thermal buckling of a rectangular cantilever plate with edge stiffeners. The case where no external loads are applied is considered, and the only stresses are those due to the prescribed thermal profile. Stiffeners are found to play an important role in the thermal buckling by affecting the overall distribution of the in-plane stresses within the plate. Results show that edge stiffeners can cause less or more buckling, and that in most situations the edge stiffeners hinder buckling because a thicker plate is required than if the stiffeners were not present.
The primary aim of this effort is to develop a software tool named “Turbomachinery Aeroelastic Analysis Tool for Forced Response (TURBOMAT-FR)” using MATLAB® (The MathWorks, Inc.) scripts. The tool will aid in performing routine forced response analysis of turbomachinery fan blades with the aid of the modal summation method (MSUM). The MSUM approach requires a modal solution consisting of modal displacements, modal frequencies, and modal stresses. The MATLAB® scripts facilitate easy extraction of the required quantities from the computational fluid dynamics (CFD) and MSC Nastran (Hexagon AB) solution files. These quantities are subsequently utilized by the MSUM approach to perform a complete forced response analysis.The MATLAB® scripts in TURBOMAT-FR are utilized in postprocessing of the MSC Nastran finite element analysis outputs in three types of solutions or steps, namely (1) stresses and displacements from static and steady response solution, (2) unsteady stresses and displacements from direct forced response solution, and (3) modal solution containing modal displacements and modal stresses. In step (4), separate MATLAB® scripts are also developed to read the processed outputs in step (3) and perform forced response analysis using MSUM. The TURBOMAT-FR MATLAB® scripts mentioned previously are presented in two reports designated “Part 1” and “Part 2”. The current report, Part 1, presents the scripts needed to accomplish steps (1) and (2), noted previously. This will be exclusively useful for performing only the static and steady response analysis and the forced response analysis using the direct forced response solution approach. Part 2 contains the TURBOMAT-FR MATLAB® scripts needed to accomplish steps (3) and (4). The MATLAB® scripts given in Part 2 facilitate the calculation of unsteady stresses using MSUM and provide an automated procedure associated with aeroelastic forced response analysis with different pressure files for the same structural model. The unsteady stresses calculated using MSUM in Part 2 can be compared with those presented in Part 1. A cantilevered blade-alone model subjected to a realistic pressure loading to a boundary was used for static and unsteady direct forced response analysis to demonstrate the effectiveness of the TURBOMATFR MATLAB® scripts.
The primary aim of this effort is to develop a software tool named “Turbomachinery Aeroelastic Analysis Tool for Forced Response (TURBOMAT-FR)” using MATLAB® (The MathWorks, Inc.) scripts. The tool will aid in performing routine forced response analysis of turbomachinery fan blades with the aid of the modal summation method (MSUM). The MSUM approach requires a modal solution consisting of modal displacements, frequencies, and stresses. The MATLAB® scripts facilitate easy extraction of the required quantities from the computational fluid dynamics (CFD) and MSC Nastran (Hexagon AB) solution files. These quantities are subsequently utilized by the MSUM approach to perform a complete forced response analysis using the MATLAB® scripts. The MATLAB® scripts in TURBOMAT-FR are utilized in postprocessing of the MSC Nastran finite element analysis outputs in three types of solutions or steps, namely (1) stresses and displacements from static or steady response solution, (2) unsteady stresses and displacements from direct forced response solution, and (3) modal solution containing modal displacements and modal stresses. In step (4), separate MATLAB® scripts are also developed to read the processed outputs in step (3) and perform forced response analysis using MSUM. It should be noted that the direct forced response solution from step (2) will provide for a comparison with those obtained from the MSUM approach in steps (3) and (4). The TURBOMAT-FR MATLAB® scripts mentioned previously are presented in two reports designated Parts 1 and 2. Part 1 presents the scripts needed to accomplish steps (1) and (2). The current report, Part 2, presents the scripts needed to accomplish steps (3) and (4), noted previously. The TURBOMAT-FR MATLAB® scripts provided here in Part 2 facilitate the calculation of unsteady stresses using MSUM and provide an automated procedure associated with aeroelastic forced response analysis with different pressure files. The unsteady stresses calculated using MSUM can be compared with those presented in Part 1. A cantilevered blade-alone model subjected to a realistic pressure loading to a boundary was used for static and unsteady direct forced response analysis to demonstrate the effectiveness of the TURBOMATFR MATLAB® scripts.