An explosion event, having a low probability of occurrence but severe consequences, due to a possible structural collapse, is a so-called "Low Probability and High Consequences (LP-HC)" event[13]. Due to the severe consequences, blast puts a great threat to public security. Thus, civil engineers should take these extreme cases into consideration during the design process to ensure the integrity of the basic frameworks of the structures to provide the possibility to the following rescue works. Nonlinear finite element analysis is a useful method for civil engineers to check the integrity of the structures under blast loading. However, there could be lots of different solution strategies for the same physical situation that may lead to differences in the corresponding numerical results. A solution strategy is a certain combination of different options in all the steps during the setting-up of the finite element model, including the definition of loads, boundary conditions, material models, element types and element sizes. Therefore, to which extent can civil engineers simulate the dynamic behavior of experiments of concrete columns with blast loading by nonlinear finite element analysis is of great interest. In this thesis, 36 different solution strategies for the same physical situation are discussed. DIANA 10.2 Educational Version is applied to generate numerical results of finite element models with different solution strategies. The modelling of boundary conditions, bond effect between steel reinforcements and concrete, blast pressure profiles and the choice of element types and the order of element on the numerical results are investigated and discussed in this thesis by dividing the 36 models into 51 groups. And the question about to which extent can we reduce the computation time while the accuracy is still satisfying is addressed.
Firstly, an investigation of literature is performed. Column CONV-7 from Test 1 of Siba’s report is selected. The blast pressure profiles at the bottom, and top of the front face of the column, and the bottom, the mid-height, and the top of the rear face of the column were recorded with pressure gauges. The displacement-time diagrams of the 1.0 m, 1.5 m and 2.0 m from the column footing of the rear face of the column were recorded while only the diagram at 1.0 m from the column footing was reliable. Then the finite element analyses with different solution strategies are performed and compared in groups. In this treatise, 36 finite element analyses with different solution strategies are performed. The numerical displacement results at 1.0 m from the column footing of the rear face of the column are compared to the experimental results.The errors of these finite element analyses with different solution strategies vary from 3.476% to 50.116%. Thus, the choice of solution strategies has a significant influence on the accuracy of the numerical results for nonlinear finite element analyses for this situation. However, there is only a limited number of solution strategies are discussed and only the displacement results at 1.0 m from the column footing are compared, therefore, the solution strategy with the lowest error may not be the most recommended one. The inclusion of the negative phases of the blast pressure profiles has an increasingly significant influence on the evaluation of the safety of those structures and structural components that are not destroyed before reaching the largest deformation in the direction of wave propagation, which differs from Karlos’ statement[17]. The modelling of damping effect with Rayleigh damping coefficients for the structures may not be very suitable, which disagrees with the example listed in the manuals of DIANA 10.2[1]. interpretation and modelling of the boundary conditions have an important influence on the numerical results, for the models with simplified geometries, modification of boundary conditions is required. The first-order elements, due to the uniform mass distributions and fewer degrees of freedom, are more recommended for both accuracy and efficiency reasons. The choice of mesh sizes in the support structure has a limited influence on the numerical results
as the support structure is less sensitive to the blast loading. The modelling of bond-slip effect between the rebars and concrete would lead to limited differences in the numerical results, this may due to the overestimation of the shear stiffness of the interface elements between the reinforcements and concrete. The finite element models with plane stress elements generally yield to a conservative result in the displacement due to the neglect of the out-of-plane deformation and the confinement of the ties is not included due to the neglect of the transverse rebars in the direction that perpendicular to the wave propagation.

Shell is a popular form of structures as it can withstand relative large load with small thickness, which satisfies the aesthetic preference. Due to the curvatures of shell structures, shell can carry the distributed load as membrane forces instead of bending moments. Due to the small thickness, shell structures are highly sensitive to imperfections. As the loads are carried by membrane forces, buckling failure often govern the design of shell structures. The buckling load could be predicted accurately by performing a nonlinear finite element analysis. However, performing a nonlinear finite element analysis is very time-consuming and expensive as a lot of computational efforts required. The currently used design formula of shell structures can lower down the requirement of computation in a great degree while the accuracy is not very satisfying. Different from other types of structures, shell buckling often starts locally, therefore, an assumption is made that shell buckling is a combination of membrane forces and curvatures. Thus, an improved buckling formula is proposed. In this report, the proposed formula is verified and optimized. In addition, the shell behaviour before buckling has been illustrated by a series of figures that show the deformation and stresses at several load steps.