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This manual documents a set of test problems used for theverification of the solvers in the Straus7 finite element analysissystem. The tests come from numerous sources as detailed in thereference section of each chapter. Each test gives the Straus7result together with the target value published in the reference.Where a percentage difference between the two is given, thispercentage is calculated using the following formula:
Straus7 Theoretical Manual
The data given in the Problem sketch of each test is intended toillustrate the problem in general terms rather than to give all thedata necessary to actually perform the test. The results given inthis edition of the manual were obtained using Straus7 Release 2.3(released in April 2004). Copies of each Straus7 model file can befound in the Verification folder of the Straus7 installation. Manyof the model files contain additional information that may beviewed using the Summary/Information menu option. The tests aredivided into 10 chapters, each covering a specific solver category:Chapter 1: Linear Static Chapter 2: Linear Buckling Chapter 3:Nonlinear Static Chapter 4: Natural Frequency Chapter 5: HarmonicResponse Chapter 6: Spectral Response Chapter 7: Linear TransientDynamic Chapter 8: Nonlinear Transient Dynamic Chapter 9: SteadyState Heat Transfer Chapter 10: Transient Heat Transfer
Grounded theory studies are characterised by theoretical sampling, but this requires some data to be collected and analysed. Sampling must thus begin purposively, as in any qualitative study. Participants in the previous MPP study provided our population [27]. The MPP included 22 private dental practices in NSW, randomly allocated to either the intervention or control group. With permission of the ethics committee; we sent letters to the participants in the MPP, inviting them to participate in a further qualitative study. From those who agreed, we used the quantitative data from the MPP to select an initial sample.
Coding is essential to the development of a grounded theory [15]. According to Charmaz [[15], p46], 'coding is the pivotal link between collecting data and developing an emergent theory to explain these data. Through coding, you define what is happening in the data and begin to grapple with what it means'. Coding occurs in stages. In initial coding, the researcher generates as many ideas as possible inductively from early data. In focused coding, the researcher pursues a selected set of central codes throughout the entire dataset and the study. This requires decisions about which initial codes are most prevalent or important, and which contribute most to the analysis. In theoretical coding, the researcher refines the final categories in their theory and relates them to one another. Charmaz's method, like Glaser's method [13], captures actions or processes by using gerunds as codes (verbs ending in 'ing'); Charmaz also emphasises coding quickly, and keeping the codes as similar to the data as possible.
We have provided a worked example of coding in Table 2. Gerunds emphasise actions and processes. Initial coding identifies many different processes. After the first few interviews, we had a large amount of data and many initial codes. This included a group of codes that captured how dentists sought out evidence when they were exposed to a complex clinical case, a new product or technique. Because this process seemed central to their practice, and because it was talked about often, we decided that seeking out evidence should become a focused code. By comparing codes against codes and data against data, we distinguished the category of "seeking out evidence" from other focused codes, such as "gathering and comparing peers' evidence to reach a conclusion", and we understood the relationships between them. Using this constant comparative method (see Table 1), we produced a theoretical code: "making sense of evidence and constructing knowledge". This code captured the social process that dentists went through when faced with new information or a practice challenge. This theoretical code will be the focus of a future paper.
We have already described our initial purposive sampling. After our initial data collection and analysis, we used theoretical sampling (see Table 1) to determine who to sample next and what questions to ask during interviews. We submitted Ethics Modification applications for changes in our question routes, and had no difficulty with approval. We will describe how the interview questions for dentists and dental practice staff evolved, and how we selected new participants to allow development of our substantive theory. The patients' interview schedule and theoretical sampling followed similar procedures.
We now had a detailed provisional model of the successful process implemented in Dental Practice 1. Important core focused codes were identified, including practical/financial, historical and philosophical dimensions of the process. However, we did not yet understand how the process might vary or go wrong, as implementation in the first practice we studied had been described as seamless and beneficial for everyone. Because our aim was to understand the process of implementing the protocols, including the conditions and consequences of variation in the process, we needed to understand how implementation might fail. For this reason, we theoretically sampled participants from Dental Practice 2, where uptake of the MPP protocols had been very limited according to data from the RCT trial.
Dentists' construction of the "unreliable" patient during interviews also prompted us to theoretically sample for "unreliable" and "reliable" patients in the following round of patients' interviews. The patient question route was also modified by the analysis of the dentists' and practice staff data. We wanted to compare dentists' perspectives with the perspectives of the patients themselves. Dentists were asked to select "reliable" and "unreliable" patients to be interviewed. Patients were asked questions about what kind of services dentists should provide and what patients valued when coming to the dentist. We found that these patients (10 reliable and 7 unreliable) talked in very similar ways about dental care. This finding suggested to us that some deeply-held assumptions within the dental profession may not be shared by dental patients.
At this point, we decided to theoretically sample dental practices from the non-intervention arm of the MPP study. This is an example of the 'openness' of a grounded theory study potentially subtly shifting the focus of the study. Our analysis had shifted our focus: rather than simply studying the process of implementing the evidence-based preventive protocols, we were studying the process of doing prevention in private dental practice. All participants seemed to be revealing deeply held perspectives shared in the dental profession, whether or not they were providing dental care as outlined in the MPP protocols. So, by sampling dentists from both intervention and control group from the previous MPP study, we aimed to confirm or disconfirm the broader reach of our emerging theory and to complete inductive development of key concepts. Theoretical sampling added 12 face to face interviews and 10 telephone interviews to the data. A total of 40 participants between the ages of 18 and 65 were recruited. Telephone interviews were of comparable length, content and quality to face to face interviews, as reported elsewhere in the literature [40].
After theoretical sampling, we could begin coding theoretically. We fleshed out each major focused code, examining the situations in which they appeared, when they changed and the relationship among them. At time of writing, we have reached theoretical saturation (see Table 1). We have been able to determine this in several ways. As we have become increasingly certain about our central focused codes, we have re-examined the data to find all available insights regarding those codes. We have drawn diagrams and written memos. We have looked rigorously for events or accounts not explained by the emerging theory so as to develop it further to explain all of the data. Our theory, which is expressed as a set of concepts that are related to one another in a cohesive way, now accounts adequately for all the data we have collected. We have presented the developing theory to specialist dental audiences and to the participants, and have found that it was accepted by and resonated with these audiences.
2. We analysed the interview transcripts as soon as possible after each round of interviews in each dental practice sampled as shown on Figure 1. This allowed the process of theoretical sampling to occur.
4. Having the opportunity to contact participants after interviews to clarify concepts and to interview some participants more than once contributed to the refinement of theoretical concepts, thus forming part of theoretical sampling.
BibliografiaO.Belluzzi. Scienza delle Costruzioni, vol. 3, cap. 26 Zanichelli, Bologna, 1960.Straus7 Theoretical Manual. Theoretical background to the Straus7 finite element analysis. Sydney : G + D Computing, 2004.Sap2000 v19.0.0. Csi analysis reference manual. Computers and Structures Inc., Berkley, California, USA,2016. 2ff7e9595c
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