| dc.description.abstract | Joints are essential to connect various components of a structural assembly. Among various methods of joining, pin (or fastener) joints are of detachable type and are the most preferred under situations requiring periodic assembly and disassembly. These joints are sources of stress concentration and are potential locations for failure. In metallic structures, the concepts of analysis and design of these joints are reasonably well established over years. The subject matter is receiving considerable attention again with the emergence of composites as structural materials in aerospace and many other engineering fields.
Pin in a plate is the basic configuration of these joints. In this thesis, a two dimensional plane stress analysis is conducted for this configuration subjected to in plane bearing and/or bypass loading. The pin is assumed to be rigid compared to the plate material. For such a configuration in infinite domains, the obvious choice for analysis is the finite element method. However, finite element modelling for this problem using conventional elements with simple polynomial interpolation functions requires a large number of elements in the region of stress concentration around the pin–hole interface. To address this, the thesis develops special finite elements (FASNEL series) in which the displacement functions are derived from complex potential functions satisfying the governing differential equation of the orthotropic domain.
Three types of FASNEL elements are developed to deal with typical pin–hole interfacial conditions and symmetries. In each case, FASNEL is an element with concentric circular boundaries, with the inner boundary coinciding with the periphery of the hole. The stiffness matrices of FASNEL elements are obtained from the principle of minimization of potential energy. The finite element model is completed by using conventional finite elements outside the FASNEL region, where stress gradients are small. Such modelling is shown to be accurate and economical for solving the stress concentration problems in pin joints.
The analysis of a pin in a plate has another intricate aspect. The pin–hole interface may be of interference, push, or clearance fit depending on whether the pin diameter is greater than, equal to, or less than the hole diameter. When the plate or pin is gradually loaded, the pin–hole interface exhibits partial contact beyond certain load levels for all three fits. This results in moving boundary value problems. For misfit pins (interference or clearance), the extent of contact/separation depends on load level, and stress concentration varies nonlinearly with load. For push fit pins, the extent of contact/separation is independent of load and the problem is linear.
Most earlier work has used iterative methods wherein, for a given load level, the contact/separation extent is determined iteratively. Significant developments have recently taken place at the Indian Institute of Science through inverse formulation, where for given extents of contact/separation, one evaluates the causative load level. In many practical problems, the nature of contact growth is known a priori, and inverse formulation is effective. In this thesis, the finite element analysis with FASNEL elements extensively uses inverse formulation, but it is also shown that FASNEL elements can be applied in situations requiring iterative or combined iterative inverse procedures.
Chapter 2 deals with the development of a continuum analysis for finite rectangular plates with a smooth pin subjected to biaxial edge loading. Complex potential functions that satisfy the differential equation for the orthotropic domain, the double symmetry of the problem, and zero shear interfacial conditions are developed. Unknown coefficients in the potential functions are obtained by successive integration of boundary errors. Unified presentation of results for interference, push, and clearance fits is demonstrated. A parametric study provides check solutions for the finite element analysis using FASNEL.
In Chapters 3, 4, and 5, three FASNEL elements are developed:
FASNEL1 – for doubly symmetric smooth interfaces (as in Chapter 2)
FASNEL2 – for singly symmetric smooth interfaces, e.g., load transfer through a smooth pin
FASNEL3 – for doubly symmetric rough interfaces (interference or clearance fits), where an arching solution is presented
The effectiveness of FASNEL elements is demonstrated through application to practical problems in composite plates under pin loading, bypass loading, and infinite rows of pins in infinite strips.
Chapter 4 demonstrates the use of FASNEL in problems requiring a combination of iterative and inverse methods. This is illustrated for a finite plate with an eccentric pin under edge loading.
The thesis is concluded in Chapter 7 with a clear assessment of achievements and limitations of the work, along with possible areas for future study. | |
