Development of a model of space station solar array

Space structures, such as the space station solar arrays, must be extremely lightweight, flexible structures. Accurate prediction of the natural frequencies and mode shapes is essential for determining the structural adequacy of components, and designing a control system. The tension preload in the blanket of photovoltaic solar collectors, and the free/free boundary conditions of a structure in space, causes serious reservations on the use of standard finite element techniques of solution. In particular, a phenomena known as grounding, or false stiffening, of the stiffness matrix occurs during rigid body rotation. The grounding phenomena is examined in detail. Numerous stiffness matrices developed by others are examined for rigid body rotation capability, and found lacking. Various techniques are used for developing new stiffness matrices from the rigorous solutions of the differential equations, including the solution of the directed force problem. A new directed force stiffness matrix developed by the author provides all the rigid body capabilities for the beam in space

Dynamic analysis of space-related linear and non-linear structures

In order to be cost effective, space structures must be extremely light weight, and subsequently, very flexible structures. The power system for Space Station Freedom is such a structure. Each array consists of a deployable truss mast and a split blanket of photovoltaic solar collectors. The solar arrays are deployed in orbit, and the blanket is stretched into position as the mast is extended. Geometric stiffness due to the preload make this an interesting non-linear problem. The space station will be subjected to various dynamic loads, during shuttle docking, solar tracking, attitude adjustment, etc. Accurate prediction of the natural frequencies and mode shapes of the space station components, including the solar arrays, is critical for determining the structural adequacy of the components, and for designing a dynamic controls system. The process used in developing and verifying the finite element dynamic model of the photo-voltaic arrays is documented. Various problems were identified, such as grounding effects due to geometric stiffness, large displacement effects, and pseudo-stiffness (grounding) due to lack of required rigid body modes. Analysis techniques, such as development of rigorous solutions using continuum mechanics, finite element solution sequence altering, equivalent systems using a curvature basis, Craig-Bampton superelement approach, and modal ordering schemes were utilized. The grounding problems associated with the geometric stiffness are emphasized

Geometric Stiffness Effects on Data Recovery of an Idealized Mast/Blanket Model

The photovoltaic arrays for the international space station consist of a pre-tensioned blanket of solar collectors and a deployable mast. NASA uses the MSC/NASTRAN finite element program for modeling the dynamic response of the structure due to various loading conditions, such as plume impingement during shuttle docking. This finite element program uses the updated stiffness matrix (elastic plus geometric, or initial stress stiffness matrix) in determining the natural frequencies and mode shapes, as well as the dynamic response, of a pre-loaded structure. However, during the data recovery phase, when the moment and shear at the supports, and internal stresses are determined, geometric stiffness effects are neglected, and only the elastic stiffness is used in the calculation. The purpose of this study was to determine whether using the actual displacements, calculated based upon both elastic and geometric stiffness effects, would produce acceptable results in predicting shear and moment if the geometric stiffness effects were later omitted during data recovery. In this study, the PV array was idealized as a cantilever beam with an attached pre-tensioned cable. Static and dynamic analysis were performed, both using and neglecting the geometric stiffness matrix during data recovery. When considering the idealized mast/blanket model, neglecting the geometric stiffness contribution during data recovery led to a 32.2% difference in the vertical (shear) load at the fixed support, and an 8.8% difference in shear at the free end of the beam (compared to the inclusion of geometric stiffness effects in the analysis). The static analysis provided similar results and supported the \u27\u27reasonableness\u27\u27 of the dynamic analysis. Due to the large discrepancies in the predicted stresses which can ocur when geometric stiffness contributions are neglected during data recovery, it should be imperative that when a structure contains pre-loaded elements, the geometric stiffness effects must be fully considered both in the determination of the natural frequencies and mode shapes, as well as in the subsequent calculation of nodal reactions and stresses

Another Look at the Collapse of Skyline Plaza at Bailey’s Crossroads, Virginia

On March 2, 1973, the Skyline Plaza apartment building in Bailey’s Crossroads, Virginia collapsed while under construction. The Occupational Health and Safety Administration (OSHA) requested an investigation from the National Bureau of Standards [(NBS); now the National Institute of Standards and Technology (NIST)]. The NBS team concluded that the most likely cause of the collapse was a punching shear failure of the 23rd floor slab. The two factors that contributed to this were premature removal of shores below the 23rd floor slab, and the low strength of the 23rd floor concrete in the area supporting the weight of the 24th floor slab. The engineer’s structural drawings required 2 full stories of shoring and 1 story of reshoring while a concrete slab was cast. The project architect and structural engineer were sued and held responsible, although their specific shoring instructions had been ignored. This case study reviews the available published information on the case to determine what lessons can be learned. The case is suitable for inclusion in variety of courses in the civil engineering and construction curriculum

1976 Montreal Olympics: Case Study of Project Management Failure

A successful engineering project must include its timely and economic completion. A project management failure can lead to delays and cost overruns. One example of a project that greatly exceeded its projected budget is the construction of the multiple facilities for the 1976 Olympic Games in Montreal. These included the Olympic Stadium, a velodrome for bicycle events, and the Olympic Village to house the athletes. This case study reviews the circumstances of the cost increases and the design decisions and other circumstances that led to them. The difficulties were brought on by an unrealistic schedule to complete the facilities before the fixed start date of the Games, combined with an unusually cavalier attitude toward project costs, exacerbated by political tensions. Although the original cost estimate for the facilities was $120 million, the final cost was$1.5 billion, with $830 million for the main stadium alone. Part of the justification for the expense of the facilities was the hope that the facilities would be useful for future athletic events—the record on this is mixed at best. The lessons learned can be applied to other projects to better control costs

A New Pre-loaded Membrane Geometric Stiffness Matrix with Full Rigid Body Capabilities

Space structures, due to economic considerations, must be light-weight. Accurate prediction of the natural frequencies and mode shapes is critical for determining the structural adequacy of components, and designing a control system. The total stiffness of a member, in many cases, includes both the elastic stiffness of the material as well as additional geometric stiffness due to pre-load (initial stress stiffness). The pre-load causes serious reservations on the use of standard finite element techniques of solution. In particular, a phenomenon known as \u27\u27grounding\u27\u27, or false stiffening, of the stiffness matrix occurs during rigid body rotation. The author has previously shown that that the grounding of a beam element is caused by a lack of rigid body rotational capability, and is typical of beam geometric stiffness matrices formulated by others, including those with higher-order effects. Having identified the source of the problem as the force imbalance inherent in the formulations, the author developed a beam stiffness matrix from a directed force perspective, and showed that the resultant global stiffness matrix contained complete rigid body mode capability, and performed well in the diagonalization methodology customarily used in dynamic analysis. In this paper, the authors investigate the \u27\u27grounding\u27\u27 of membrane elements, and develop a new membrane element with rigid body rotational capabilities

A New Pre-loaded Membrane Geometric Stiffness Matrix with Full Rigid Body Capabilities

Space structures, due to economic considerations, must be light-weight. Accurate prediction of the natural frequencies and mode shapes is critical for determining the structural adequacy of components, and designing a control system. The total stiffness of a member, in many cases, includes both the elastic stiffness of the material as well as additional geometric stiffness due to pre-load (initial stress stiffness). The pre-load causes serious reservations on the use of standard finite element techniques of solution. In particular, a phenomenon known as \u27\u27grounding\u27\u27, or false stiffening, of the stiffness matrix occurs during rigid body rotation. The author has previously shown that that the grounding of a beam element is caused by a lack of rigid body rotational capability, and is typical of beam geometric stiffness matrices formulated by others, including those with higher-order effects. Having identified the source of the problem as the force imbalance inherent in the formulations, the author developed a beam stiffness matrix from a directed force perspective, and showed that the resultant global stiffness matrix contained complete rigid body mode capability, and performed well in the diagonalization methodology customarily used in dynamic analysis. In this paper, the authors investigate the \u27\u27grounding\u27\u27 of membrane elements, and develop a new membrane element with rigid body rotational capabilities

Another Look at the Collapse of Skyline Plaza at Bailey’s Crossroads, Virginia

On March 2, 1973, the Skyline Plaza apartment building in Bailey’s Crossroads, Virginia collapsed while under construction. The Occupational Health and Safety Administration (OSHA) requested an investigation from the National Bureau of Standards [(NBS); now the National Institute of Standards and Technology (NIST)]. The NBS team concluded that the most likely cause of the collapse was a punching shear failure of the 23rd floor slab. The two factors that contributed to this were premature removal of shores below the 23rd floor slab, and the low strength of the 23rd floor concrete in the area supporting the weight of the 24th floor slab. The engineer’s structural drawings required 2 full stories of shoring and 1 story of reshoring while a concrete slab was cast. The project architect and structural engineer were sued and held responsible, although their specific shoring instructions had been ignored. This case study reviews the available published information on the case to determine what lessons can be learned. The case is suitable for inclusion in variety of courses in the civil engineering and construction curriculum

Dynamic Analysis of Space-Related Linear and Nonlinear Structures

In order to be cost-effective, space structures must be extremely light-weight, and subsequently, very flexible structures, The power system for Space Station \u27Freedom\u27 is such a structure. Each array consists of a deployable truss mast and a split \u27blanket\u27 of photo-voltaic solar collectors. The solar arrays are deployed in orbit, and the blanket is stretched into position as the mast is extended. Geometric stiffness due to the preload make this an interesting non-linear problem. The space station will be subjected to various dynamic loads, during shuttle docking, solar tracking, attitude adjustment, etc. Accurate prediction of the natural frequencies and mode shapes of the space station components, including the solar arrays, is critical for determining the structural adequacy of the components, and for designing a dynamic controls system. This paper chronicles the process used in developing and verifying the finite element dynamic model of the photo-voltaic arrays. Various problems were identified in the investigation, such as grounding effects due to geometric stiffness, large displacement effects, and pseudo-stiffness (grounding) due to lack of required rigid body modes. Various analysis techniques, such as development of rigorous solutions using continuum mechanics, finite element solution sequence altering, equivalent systems using a curvature basis, Craig-Bampton superelement approach, and modal ordering schemes were utilized. This paper emphasizes the grounding problems associated with the geometric stiffness

Grounding of Space Structures

Space structures, such as the Space Station solar arrays, must be extremely light-weight, flexible structures. Accurate prediction of the natural frequencies and mode shapes is essential for determining the structural adequacy of components, and designing a controls system. The tension pre-load in the \u27blanket\u27 of photovoltaic solar collectors, and the free/free boundary conditions of a structure in space, causes serious reservations on the use of standard finite element techniques of solution. In particular, a phenomenon known as \u27grounding\u27, or false stiffening, of the stiffness matrix occurs during rigid body rotation. This paper examines the grounding phenomenon in detail. Numerous stiffness matrices developed by others are examined for rigid body rotation capability, and found lacking. A force imbalance inherent in the formulations examined is the likely cause of the grounding problem, suggesting the need for a directed force formulation