K. L. Lawrence

Micromachined integrated pressure—thermal sensors on flexible substrates

This paper presents the design, modeling and simulation of micromachined, integrated pressure–thermal sensors on flexible polyimide substrates. Finite element simulations were performed with polycrystalline silicon as the piezoresistor material on a suspended Si3N4 layer. These piezoresistors are connected to each other in a half-bridge Wheatstone configuration using flexible aluminum interconnects. Several different designs of integrated thermal–pressure sensors as well as pressure-only sensors were simulated to compute the sensor figures of merit such as the percentage change in piezoresistance in response to normal pressure, piezoresistor Wheatstone-bridge output voltage for varying skin curvature, bolometric response to broadband infrared radiation, thermal time constant and thermal conductance of the micromachined structures hosting the sensors to the substrate. For a perpendicular uniform pressure application of 50 kPa, a maximum Wheatstone-bridge output of 7.59 mV was computed for 1 V bias, corresponding to a piezoresistance change of 1.52%. When the skin is bent to a curvature of 2.2 mm, a maximum Wheatstone-bridge output voltage of 70 mV was calculated for the case when the sensors are aligned along the axis of bending. Thermal and optical calculations performed on the integrated thermal–pressure sensors showed a thermal time constant as low as 12.8 µs for a 1.9 µm thick silicon nitride membrane layer, with a responsivity of 270 V W−1 to a broad-band infrared radiation. This would be appropriate for applications requiring fast response but not high sensitivity. Integrated sensors on a thinner silicon nitride membrane layer of 0.5 µm, on the other hand, exhibited responsivity as high as 2000 V W−1, with a response time of 626 µs.

Simple algorithm for adaptive refinement of three-dimensional finite element tetrahedral meshes

A simple strategy to adaptively refine three-dimensional tetrahedral meshes has been implemented. The procedure adaptively refines a crude initial mesh using solution error indicators or other suitable measures. In this paper example problems were remeshed using a refinement ratio determined from an a posteriori error indicator obtained from the finite element solution or the problem. The resulting finite element meshes are round to have a smooth gradient in element size. Aspect ratios are calculated to determine the quality or each element, and a smoothing procedure is employed to improve the element aspect ratio. Example meshes are included to show the adaptive nature or the remesher when applied over several solution cycles

Elastic wave generation by piezoceramic patches

Elastic flexural and longitudinal waves can be generated in structure by using piezoelectric transducers. These waves may be used to obtain fundamental properties of the medium or to locate flaws. Bulk waves can be created in a thin piezoelectric plate by applying an electrical signal to interdigital electrodes deposited on each side of the plate. These transducers can be used to generate ultrasonic bulk waves with a wide range of frequencies and amplitudes controlled by a number of electrodes and a delayed voltage independently applied to each electrode. Numerical results demonstrating the finite element simulation of piezoelectric actuators and sensors in generating and detecting elastic bulk waves are presented. Experimental observations of flexural waves generated hy surface mounted piezoceramic plates are compared with the finite element results. Bulk wave generation and detection using interdigital electrodes are simulated and their potential application as probes in smart structures is discussed.

Closed-form stiffness matrices for the linear strain and quadratic strain tetrahedron finite elements

Abstract In this paper the development of closed-form representations of element stiffness matrices and the equivalent nodal loads for the linear strain and quadratic strain straight edge tetrahedral elements are presented. The closed-form representation of the element stiffness matrix and the equivalent nodal loads were performed using symbolic algebra. Dramatic time savings result in the element stiffness matrix evaluation phase of the FEM process when the closed-form representation is used as compared with the use of Gaussian quadrature.

Closed-form expressions for the linear and quadratic strain tetrahedral finite elements

Abstract The use of closed-form expressions in a finite element code significantly reduces the time required to evaluate the element stiffness matrix as compared to Gaussian quadrature. The development of closed-form expressions for the element stiffness matrices for the plane-faced linear strain and quadratic strain tetrahedral finite elements has been previously presented elsewhere. In this paper, a reformulation of the process is given which significantly reduces the size of the element stiffness expressions. Expression growth is prevented by decomposing the strain-displacement matrix and utilizing a new matrix which is geometry and material dependent.

Damage assessment based on the structural frequency-response function

A method is presented for determining both the amount and position of damage present in members which can be modeled as longitudinally vibrating uniform beams. The method is valid for all boundary conditions, and for simplicity, is applied to the free-free case. It uses the shift in the natural frequencies of vibration, which are determined from the structural frequency-response function, caused by the damage present in the beam. These altered values of frequency are then utilized in a graphical solution technique which predicts the damage location directly and provides a parameter whose value is related to the magnitude of the damage present.

Closed-Form Expressions for Higher Order Electroelastic Tetrahedral Elements

A finite element formulation for three-dimensional modeling of dynamic and static responses of structures with piezoelectric components and the development of highly efficient closed-form expressions for element electroelastic stiffness matrices for straight-sided linear strain tetrahedral and quadratic strain tetrahedral elements are presented. Included is a discussion of procedures for combining tetrahedra to produce hexahedral elements. Two simple numerical examples are presented to illustrate the formulation.

Two-dimensional finite element mesh generation based on stripwise automatic triangulation

Abstract A new mesh generator, capable of discretizing arbitrary, two-dimensional, multiply connected domains into triangles with a prescribed spatial density, has been developed. The technique is based on stripwise automatic triangulation. The triangulation strategy has been enhanced using two heuristics. The first is a method to temporarily reorient a region before submitting it for generation. The second is a technique to find and repair ‘omitted patches’ near sharply curved boundaries. Despite employing a set of heuristics, the resulting scheme is versatile, robust and demonstrates a near linear growth rate.

Closed-form stiffness matrices for higher order tetrahedral finite elements

Closed-form expressions for straight-sided isoparametric tetrahedral finite element stiffness matrices up to p-level 3 have been shown to offer significant time savings when compared to numerical integration. In this work, the development of closed-form stiffness matrices is extended to the next level of approximation, the subparametric p-level 4 element. The resulting stiffness matrices are verified, and computational efficiency was tested by comparing floating-point operations required for closed-form and numerically integrated solutions. Results showed that closed-form elements still provide time savings in stiffness matrix evaluation for all p-levels tested, with up to 61x speed gain for p-level 4 depending on the compiler used. It was also found that the compilers used could better optimize the code with closed form generated expressions for efficient execution when compared to the code for numerical integration.

A study of adaptively remeshed finite element problems using higher order tetrahedra

Abstract A study has been performed for various three-dimensional elasticity problems to evaluate the performance of a three-dimensional FEM preprocessor, processor and companion remeshing modules. Both straight-sided and curve-sided tetrahedral finite elements were employed. All the problems analyzed started with initial meshes varying from 5 to 20 linear strain or quadratic strain tetrahedral elements. Remeshing was based on Zienkiewicz-Zhu error indicators obtained from the processor. The modules were used iteratively for each problem until the estimated error converged to a user specified value. Comparisons based on accuracy, convergence and computational efficiency were performed for all problems and element combinations.