The transient response of various plate structures subject to blast loads is analyzed. In particular, simply supported isotropic and laminated composite plates are modeled using the commercial finite element code NASTRAN and the method of modal superposition. Both analysis procedures are used to quantify the linear transient response of such plates subject to uniform and patch blast loads. Furthermore, NASTRAN is used to study the nonlinear response of plates subject to close proximity explosions. Also considered here is the case for which a blast loaded plate impacts another closely neighboring plate. The NASTRAN solution used here accounts for nonlinearities due to large plate deflections, plasticity, and plate-to-plate contact. Many studies are currently available in which the blast load is considered to be spatially uniform across the plate; with a temporal distribution described by step, N-pulse, or Friedlander equations. The novel aspect considered here is the case for which the blast pressure is due to a close proximity explosion, and it is therefore taken to be both spatially and temporally varying. A FORTRAN program is described which automates the application of an arbitrary blast load to a generic finite element mesh. The results presented here are a collection of analyses performed for a variety of parameters important to the dynamic response of blast loaded contacting plates. Conclusions are drawn concerning the influence of the various parameters on the nature of the plate response and the quality of the solution. / Master of Science

The purpose of this Master thesis is to evaluate the RFEM software and determine if it could be used for dynamic analyses using blast loads from explosions. Determining the blast resistance for a structure is a growing market and would therefore be beneficial for Sweco Eskilstuna if RFEM could be used for this type of work. The verification involved comparing the RFEM software to a real experiment which consisted of a set of blast tested reinforced concrete beams. By using the structural properties from the experiment project with the experiment setup the same structure could be replicated in RFEM. RFEM would then simulate a dynamic analysis loaded with the same dynamic load measured from the experiment project in two different dynamic load cases caused by two differently loaded explosions. The structural response from the experiment could then be compared to the response simulated by the RFEM software, which consisted of displacement- and acceleration time diagrams. By analysing the displacement and acceleration of both the experiment and the RFEM software the accuracy was determined, and how well RFEM preformed the analysis for this specific situation. The comparison of the displacement and acceleration between the experiment and RFEM was considered acceptable if the maximum displacement was consistent with the experiments result and within the same time frame. The acceleration was considered acceptable if the initial acceleration was consistent with the experiment result. These criteria needed to be met for the verification that RFEM could simulate a dynamic analysis. If the software managed to complete a dynamic analysis for two dynamic load cases, then the software could be evaluated which consisted of determining if the post blast effects could be determined and if the modelling method was reliable.  The acceleration from RFEM were in good agreement with the experiment test at the initial part of the blast, reaching a close comparison for both load cases after 3 ms. Then the RFEM acceleration had a chaotic behaviour reaching no similarities for the duration of the blast. The displacement managed to get a close comparison of the maximum displacement with a margin of 0,5 mm for both load cases within a 1 ms time margin. RFEM managed in conclusion to simulate a blast load analysis, the displacement and acceleration gave acceptable results according to the criteria.  With the method chosen a fast simulation was achieved and with the same model complying with two different load cases for the same model gave indication that the first result was not a coincidence. The steps taken in the modelling method was straight forward, but two contributing parameters were determined to devalue the reliability. First parameter was the material model chosen for the concrete, which was chosen to a plastic material model. The two optional material model’s linear elastic and non-linear elastic both caused failed simulations. Also, the better model for the material model would have been a diagram model which insured that the concrete lost is capacity in tension with maximum capacity, but this was not available in a dynamic analysis with multiple load increments. Which is the reason why a plastic material model was chosen for the concrete. The second reason was the movement of the beam in the supports. This data was not recorded in the experiment but was determined to be a contributing part of the test. This however gave big differences of the result depending on how much the beam could move. In the end the best possible result was chosen to comply with the first load case where the same RFEM model was used in the second test. The second load case showed just as good results as the first load case, but with the big variation in results depending on the movement of the beam in the supports made this part unclear.  For the evaluation the question if the RFEM could provide a post blast analysis needed to be addressed, where the answer is no. The failure mode was chosen to comply with the choice of modelling method which required the analysis of the plastic strain in the reinforcement bars. This information was not available using the add-on module DYNAM-PRO and could therefore not provide the answer if the model structure resisted the blast.  For future work of this master thesis is to build a model that would give a more detailed post blast analysis, where this thesis was made to test the software. For this more work would be necessary by the creators Dlubal to further improve the add-on-module, which involves more extractable results and more detailed tools when using a dynamic load case, where some important functionality is only usable in a static load case. Other than that, RFEM managed to complete the dynamic analysis, and with further improving of the modelling method a more detailed analysis can be made and then be usable in real projects in the future.

This research developed the quasi-static and dynamic equipment and protocols for tests of both Very-High-Strength Concrete (VHSC) and High-Strength High-Ductility Concrete (HSHDC) to predict blast performance. VHSC was developed for high compressive strength (> 200 MPa). Using VHSC as the baseline material, HSHDC was developed and exhibits comparable compressive strength (> 150 MPa) and high tensile ductility (> 3% tensile strain). This research investigated quasi-static material properties including compression, tension, and flexure (third-point and pressure loadings). Additionally, dynamic blast load simulator (shock tube) tests were performed on simply-supported one-way panels in flexure. Subsequently, the material response in flexure was predicted using the Wall Analysis Code (WAC). Although VHSC has a higher peak flexural strength capacity, HSHDC exhibits higher ductility through multiple parallel micro-cracks transverse to loading. The equipment and test protocols proved to be successful in providing ways to test scaled concrete specimens quasi-statically and dynamically.

Structural systems have been evolving in terms of material properties and construction techniques, and their levels of protection against hazardous events have been the focus of different studies. For instance, the performance of the lateral force resisting systems has been investigated extensively to ensure that such systems would provide an adequate level of strength ductility capacity when subjected to seismic loading. However, with the increased occurrence of accidental and deliberate explosion incidents globally by more than three fold from 2004 to 2012, more studies have been focusing on the performance of such systems to blast loads and the different methods to quantify the inflicted damage. Although both blast and seismic design requires structures to sustain a level of ductility to withstand the displacement demands, the distributions of such demands from seismic ground excitation and blast loading throughout the structural system are completely different. Therefore, a ductile seismic force resisting system may not necessarily be sufficient to resist a blast wave. To address this concern, North American standards ASCE 59-11, CSA S850-12 provide response limits that define the different damage states that components may exhibit prior to collapse. Over the past ten years, a new configuration of reinforced masonry (RM) shear walls utilizing boundary elements (BEs) at the vertical edges of the wall has been investigated as an innovative configuration that enhances the wall’s in-plane performance. As such, they are included in the North American Masonry design standards, CSA S304-14 and TMS 402-16 as an alternative means to enhance the ductility of seismic force resisting systems. However, investigations regarding the out-of-plane performance of such walls are generally scarce in literature which hindered the blast design standards from providing unique response limits that can quantify the different damage states for RM walls with BEs. This dissertation has highlighted that some relevant knowledge gaps may lead to unconservative designs. Such gaps include (a) the RM wall with BEs out-of-plane behavior and damage sequence; and more specifically, (b) the BEs influence on the wall load-displacement response; as well as, (c) the applicability of using of the current response limits originally assigned for conventional RM walls to assess RM walls with BEs. Addressing these knowledge gaps is the main motivation behind this dissertation. In this respect, this dissertation reports an experimental program, that focuses on bridging the knowledge gap pertaining to the out-of-plane performance of seismically-detailed RM shear walls with BEs, which were not designed to withstand blast loads. Meanwhile, from the analytical perspective, plastic analyses were carried out taking into account the different mechanisms that the wall may undergo until peak resistance is achieved. This approach was adopted in order to quantify the resistance function of such walls and determine the contribution of the BEs and web to the overall wall resistance. In addition, the experimental results of the tested walls were used to validate a numerical finite element model developed to compare the resistance function of RM walls with and without BEs. Afterwards, the model was further refined to capture the walls’ performance under blast loads. The pressure impulse diagrams were generated to assess the capability of the current response limits in quantifying the different damage states for walls with different design parameters. Furthermore, new response limits were proposed to account for the out-of-plane ductility capacities of different wall components. Finally, a comparison between conventional rectangular walls and their counterparts with BEs using the proposed limits was conducted in the form of pressure-impulse diagram to highlight the major differences between both wall configurations. / Thesis / Doctor of Philosophy (PhD)

This master's thesis is focused on the structural response due to blast loading, where the geometry used was arbitrary but heavily inspired by Siemens Energy. The aim of the thesis is to gain a better understanding on how to model the blast load and how it affects the structure, as well as to study the modeling of bolts with both pre-tension and a damage criteria in an explicit analysis. Lastly, the importance of strain rate dependent material models was studied. Other aspects such as mass scaling and Rayleigh damping were also investigated. The software used to solve these tasks were Hypermesh, Abaqus and Python. To conclude, the conclusions drawn from this thesis was that bolts should be modeled using connector elements, and including pre-tension is more conservative than not using it for the case studied. However, for the material modeling it gives more conservative results when using a strain rate independent material model compared to the strain rate dependent model, and is advised to be used in the future.

Curtain walls provide exterior façade to modern buildings. When subjected to blast shock waves, curtain walls may suffer significant damage, potentially causing serious injuries and casualties to building occupants. Protective films, laminated glass and strengthening of mullions and transoms are used to protect curtain wall components against blast loads. Limited research is available on blast protection of curtain wall components. On the other hand, connections of curtain wall mullions with the supporting substrate, as well as mullion-transom connections form potentially vulnerable locations under blast loads. Research on these connections is lacking in the literature. Therefore, a comprehensive research project has been undertaken in this thesis to address the behavior, analysis, and design of curtain wall connections, both between the mullions and supporting concrete slabs/beams and the mullions and transoms. The research project consists of three phases: i) Experimental research using the University of Ottawa Shock Tube as blast simulator, ii) Numerical investigation based on three-dimensional finite element method (FEM) using LS-DYNA, and iii) Non-linear dynamic analysis of curtain wall systems based on a single-degree-of-freedom (SDOF) to develop a connection design procedure. The experimental phase consisted of tests of three full-size curtain walls mounted on steel HSS sections of the Shock Tube to investigate mullion-to-transom connections and nine single mullions connected to concrete beams to investigate mullion-to-concrete substrate connection. The single mullions either represented floor-to-floor mullions or continuous mullions over the supporting slab. They were connected to concrete beams (representing floor slabs) by means of brackets, which provided high degree of rotational restraints and full translational restraints or connected through damping materials (springs or HRD rubber pads), which allowed translational movements as they dampened the effects of the shock wave. The numerical investigation involved FEM analysis and modeling of all the test specimens. The first step involved the validation of numerical models against test data. The analysis was then extended to conduct a parametric investigation to cover cases that have not been covered in the experiments. This resulted in the investigation of six different design parameters used in connection design. The numerical outcomes illustrated the importance of blast effects on connection design parameters, support reactions, curtain wall response, force and stress distributions on curtain wall components. The information gathered through experimental and numerical research on connection performance led to the formulation of a connection design procedure. Single-degree-of-freedom (SDOF) dynamic analysis technique was adopted to curtain wall analysis as a tool to compute connection design forces. Both the Uniform Facilities Criteria (UFC) charted solution (manual calculations) and two computer software developed at the University of Ottawa (RC-Blast and CW-Blast) were used to conduct SDOF analysis to validate the procedure against experimental and numerical results before they were recommended as design tools. Finally, the details of connection design are provided for different types of connections.

Due to high specific strength and stiffness as well as outstanding energy-absorption characteristics, sandwich structures are extensively used in aircraft, aerospace, automobile, and marine industries. With the objective of finding lightweight blast-resistant sandwich structures for protecting infrastructure, we have found, for a fixed areal mass density, one- or two-core doubly-curved sandwich shell's (plate's) geometries and materials and fiber angles of unidirectional fiber-reinforced face sheets for it to have the maximum first failure load under quasistatic (blast) loads. The analyses employ a third-order shear and normal deformable plate/shell theory (TSNDT), the finite element method (FEM), a stress recovery scheme (SRS), the Tsai-Wu failure criterion and the Nest-Site selection (NeSS) optimization algorithm, and assume the materials to be linearly elastic. For a sandwich shell under the spatially varying static pressure on the top surface, the optimal non-symmetric one-core (two-core) design improves the first failure load by approximately 33% (27%) and 50% (36%) from the corresponding optimal symmetric design with clamped and simply-supported edges, respectively. For a sandwich plate under blast loads, it is found that the optimal one-core design is symmetric about the mid-surface with thick face sheets, and the optimal two-core design has a thin middle face sheet and thick top and bottom face sheets. Furthermore, the transverse shear stresses (in-plane transverse axial stresses) primarily cause the first failure in a core (face sheet). For the computed optimal design under a blast load, we also determined the collapse load by using the progressive failure analysis that degrades all elasticities of the failed material point to very small values. The collapse load of the clamped (simply-supported) sandwich structure is approximately 15%–30% (0%–17%) higher than its first failure load. Incompressible materials such as rubbers, polymers, and soft tissues that can only undergo volume preserving deformations have numerous applications in engineering and biomedical fields. Their vibration characteristics are important for using them as wave reflectors at interfaces with a fiber-reinforced sheet. In this work we have numerically analyzed free vibrations of plates made of a linearly elastic incompressible rubber-like material (Poison's ratio = 0.5) by using a TSNDT for incompressible materials and the mixed FEM. The displacements at nodes of a 9-noded quadrilateral element and the hydrostatic pressure at four interior nodes are taken as unknowns. Computed results are found to match well with the corresponding either analytical or numerical ones obtained with the commercial FE software Abaqus and the 3-dimensional linear elasticity theory. The analysis discerns plate's in-plane vibration modes. It is found that a simply supported plate admits more in-plane modes than the corresponding clamped and clamped-free plates. / Doctor of Philosophy / A simple example of a sandwich structure is a chocolate ice cream bar with the chocolate layer replaced by a stiff plate. Another example is the packaging material used to protect electronics during shipping and handling. The intent is to find the composition and the thickness of the "chocolate layer" so that the ice cream bar will not shatter when dropped on the floor. The objective is met by enforcing the chocolate layer with carbon fibers and then finding fiber materials, their alignment, ice cream or core material, and its thickness to resist anticipated loads with a prescribed level of certainty. Thus, a sandwich structure is usually composed of a soft thick core (e.g., foam) bonded to two relatively stiff thin skins (e.g., made of steel, fiber-reinforced composite) called face sheets. They are lightweight, stiff, and effective in absorbing mechanical energy. Consequently, they are often used in aircraft, aerospace, automobile, and marine industries. The load that causes a point in a structure to fail is called its first failure load, and the load that causes it to either crush or crumble is called the ultimate load. Here, for a fixed areal mass density (mass per unit surface area), we maximize the first failure load of a sandwich shell (plate) under static (dynamic) loads by determining its geometric dimensions, materials and fiber angles in the face sheets, and the number (one or two) of cores. It is found that, for a non-uniformly distributed static pressure applied on the central region of a sandwich shell's top surface, an optimal design that has different materials for the top and the bottom face sheets improves the first failure load by nearly 30%-50% from that of the optimally designed structure with identical face sheets. For the structure optimally designed for the first failure blast load, the ultimate failure load with all of its edges clamped (simply supported) is about 15%-30% (0%-17%) higher than its first failure load. This work should help engineers reduce weight of sandwich structures without sacrificing their integrity and save on materials and cost. Rubberlike materials, polymers, and soft tissues are incompressible since their volume remains constant when they are deformed. Plates made of incompressible materials have a wide range of applications in everyday life, e.g., we hear because of vibrations of the ear drum. Thus, accurately predicting their dynamic behavior is important. A first step usually is determining natural frequencies, i.e., the number of cycles of oscillations per second (e.g., a human heart beats at about 1 cycle/sec) completed by the structure in the absence of any externally applied force. Here, we numerically find natural frequencies and mode shapes of rubber-like material rectangular plates with different supporting conditions at the edges. We employ a plate theory that reduces a 3-dimensional (3-D) problem to a 2-D one and the finite element method. The problem is challenging because the incompressibility constraint requires finding the hydrostatic pressure as a part of the problem solution. We show that the methodology developed here provides results that match well with the corresponding either analytical or numerical solutions of the 3-D linear elasticity equations. The methodology is applicable to analyzing the dynamic response of composite structures with layers of incompressible materials embedded in it.

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